[
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -0.44967,
        "lon": -76.99724,
        "name": "Puerto Francisco de Orellana"
      },
      {
        "lat": 5.33573,
        "lon": -72.3939,
        "name": "Yopal"
      },
      {
        "lat": 9.03934,
        "lon": -69.73364,
        "name": "Guanare"
      },
      {
        "lat": 10.31899,
        "lon": -65.97751,
        "name": "Río Chico"
      },
      {
        "lat": 6.24924,
        "lon": -57.51578,
        "name": "New Amsterdam"
      }
    ],
    "ground_truth": {
      "area_km2": 1006342.34,
      "perimeter_km": 5084.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Puerto Francisco de Orellana: (-0.4497°, -76.9972°)",
      "  Yopal: (5.3357°, -72.3939°)",
      "  Guanare: (9.0393°, -69.7336°)",
      "  Río Chico: (10.3190°, -65.9775°)",
      "  New Amsterdam: (6.2492°, -57.5158°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5084.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1006342.34 km²",
      "FINAL ANSWER: Area: 1006342.34 km², Perimeter: 5084.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -38.15912,
        "lon": 145.93118,
        "name": "Warragul"
      },
      {
        "lat": -37.91667,
        "lon": 145.11667,
        "name": "Clayton"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      },
      {
        "lat": -26.66008,
        "lon": 153.09953,
        "name": "Maroochydore"
      },
      {
        "lat": -34.06251,
        "lon": 151.14961,
        "name": "Cronulla"
      }
    ],
    "ground_truth": {
      "area_km2": 173622.32,
      "perimeter_km": 3033.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Warragul: (-38.1591°, 145.9312°)",
      "  Clayton: (-37.9167°, 145.1167°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "  Maroochydore: (-26.6601°, 153.0995°)",
      "  Cronulla: (-34.0625°, 151.1496°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3033.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 173622.32 km²",
      "FINAL ANSWER: Area: 173622.32 km², Perimeter: 3033.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.29167,
        "lon": 127.50778,
        "name": "Pubal"
      },
      {
        "lat": 38.42194,
        "lon": 140.30833,
        "name": "Yachi"
      },
      {
        "lat": 35.38329,
        "lon": 139.93254,
        "name": "Kisarazu"
      }
    ],
    "ground_truth": {
      "area_km2": 190343.84,
      "perimeter_km": 2601.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pubal: (37.2917°, 127.5078°)",
      "  Yachi: (38.4219°, 140.3083°)",
      "  Kisarazu: (35.3833°, 139.9325°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2601.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 190343.84 km²",
      "FINAL ANSWER: Area: 190343.84 km², Perimeter: 2601.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.06217,
        "lon": 114.49272,
        "name": "Xingtai"
      },
      {
        "lat": 37.80822,
        "lon": 120.75908,
        "name": "Dengzhou"
      },
      {
        "lat": 35.94389,
        "lon": 126.95444,
        "name": "Iksan"
      },
      {
        "lat": 35.37111,
        "lon": 139.22361,
        "name": "Hadano"
      },
      {
        "lat": 33.5547,
        "lon": 131.72796,
        "name": "Kunisaki"
      },
      {
        "lat": 32.84111,
        "lon": 130.04306,
        "name": "Isahaya"
      }
    ],
    "ground_truth": {
      "area_km2": 638976.1,
      "perimeter_km": 4640.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Xingtai: (37.0622°, 114.4927°)",
      "  Dengzhou: (37.8082°, 120.7591°)",
      "  Iksan: (35.9439°, 126.9544°)",
      "  Hadano: (35.3711°, 139.2236°)",
      "  Kunisaki: (33.5547°, 131.7280°)",
      "  Isahaya: (32.8411°, 130.0431°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4640.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 638976.10 km²",
      "FINAL ANSWER: Area: 638976.10 km², Perimeter: 4640.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -32.48463,
        "lon": -58.23217,
        "name": "Concepción del Uruguay"
      },
      {
        "lat": -24.00306,
        "lon": -53.70417,
        "name": "Iporã"
      },
      {
        "lat": -19.98639,
        "lon": -44.42778,
        "name": "Mateus Leme"
      },
      {
        "lat": -23.52917,
        "lon": -47.13528,
        "name": "São Roque"
      },
      {
        "lat": -23.56786,
        "lon": -46.54599,
        "name": "Vila Formosa"
      }
    ],
    "ground_truth": {
      "area_km2": 466885.94,
      "perimeter_km": 4154.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Concepción del Uruguay: (-32.4846°, -58.2322°)",
      "  Iporã: (-24.0031°, -53.7042°)",
      "  Mateus Leme: (-19.9864°, -44.4278°)",
      "  São Roque: (-23.5292°, -47.1353°)",
      "  Vila Formosa: (-23.5679°, -46.5460°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4154.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 466885.94 km²",
      "FINAL ANSWER: Area: 466885.94 km², Perimeter: 4154.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.47797,
        "lon": 91.1055,
        "name": "Damxung"
      },
      {
        "lat": 34.8975,
        "lon": 105.18639,
        "name": "Dashi"
      },
      {
        "lat": 34.98756,
        "lon": 106.20902,
        "name": "Zhangjiachuan"
      }
    ],
    "ground_truth": {
      "area_km2": 11614.91,
      "perimeter_km": 2995.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Damxung: (30.4780°, 91.1055°)",
      "  Dashi: (34.8975°, 105.1864°)",
      "  Zhangjiachuan: (34.9876°, 106.2090°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2995.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 11614.91 km²",
      "FINAL ANSWER: Area: 11614.91 km², Perimeter: 2995.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 23.58645,
        "lon": 56.53969,
        "name": "Yanqul"
      },
      {
        "lat": 31.34082,
        "lon": 69.4493,
        "name": "Zhob"
      },
      {
        "lat": 24.85822,
        "lon": 69.40153,
        "name": "Naukot"
      }
    ],
    "ground_truth": {
      "area_km2": 473938.53,
      "perimeter_km": 3568.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Yanqul: (23.5864°, 56.5397°)",
      "  Zhob: (31.3408°, 69.4493°)",
      "  Naukot: (24.8582°, 69.4015°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3568.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 473938.53 km²",
      "FINAL ANSWER: Area: 473938.53 km², Perimeter: 3568.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 10.11135,
        "lon": -63.09985,
        "name": "Caripito"
      },
      {
        "lat": 5.86638,
        "lon": -55.16682,
        "name": "Paramaribo"
      },
      {
        "lat": -10.22306,
        "lon": -54.97972,
        "name": "Peixoto de Azevedo"
      }
    ],
    "ground_truth": {
      "area_km2": 783444.58,
      "perimeter_km": 5214.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Caripito: (10.1113°, -63.0999°)",
      "  Paramaribo: (5.8664°, -55.1668°)",
      "  Peixoto de Azevedo: (-10.2231°, -54.9797°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5214.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 783444.58 km²",
      "FINAL ANSWER: Area: 783444.58 km², Perimeter: 5214.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.63222,
        "lon": -48.68472,
        "name": "Barra Velha"
      },
      {
        "lat": -20.94944,
        "lon": -48.47917,
        "name": "Bebedouro"
      },
      {
        "lat": -15.0725,
        "lon": -57.18111,
        "name": "Barra do Bugres"
      },
      {
        "lat": -9.56722,
        "lon": -48.39167,
        "name": "Miracema do Tocantins"
      },
      {
        "lat": -12.74083,
        "lon": -38.62083,
        "name": "Madre de Deus"
      },
      {
        "lat": -23.3075,
        "lon": -47.13278,
        "name": "Cabreúva"
      }
    ],
    "ground_truth": {
      "area_km2": 2294286.55,
      "perimeter_km": 5897.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Barra Velha: (-26.6322°, -48.6847°)",
      "  Bebedouro: (-20.9494°, -48.4792°)",
      "  Barra do Bugres: (-15.0725°, -57.1811°)",
      "  Miracema do Tocantins: (-9.5672°, -48.3917°)",
      "  Madre de Deus: (-12.7408°, -38.6208°)",
      "  Cabreúva: (-23.3075°, -47.1328°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5897.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2294286.55 km²",
      "FINAL ANSWER: Area: 2294286.55 km², Perimeter: 5897.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.10415,
        "lon": -113.58412,
        "name": "Saint George"
      },
      {
        "lat": 42.49999,
        "lon": -96.40031,
        "name": "Sioux City"
      },
      {
        "lat": 44.73191,
        "lon": -93.21772,
        "name": "Apple Valley"
      },
      {
        "lat": 43.63552,
        "lon": -79.50113,
        "name": "Stonegate-Queensway"
      },
      {
        "lat": 42.99812,
        "lon": -78.18752,
        "name": "Batavia"
      },
      {
        "lat": 38.47841,
        "lon": -82.63794,
        "name": "Ashland"
      }
    ],
    "ground_truth": {
      "area_km2": 1390925.36,
      "perimeter_km": 6503.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Saint George: (37.1041°, -113.5841°)",
      "  Sioux City: (42.5000°, -96.4003°)",
      "  Apple Valley: (44.7319°, -93.2177°)",
      "  Stonegate-Queensway: (43.6355°, -79.5011°)",
      "  Batavia: (42.9981°, -78.1875°)",
      "  Ashland: (38.4784°, -82.6379°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6503.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1390925.36 km²",
      "FINAL ANSWER: Area: 1390925.36 km², Perimeter: 6503.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 18.54326,
        "lon": -92.6453,
        "name": "Frontera"
      },
      {
        "lat": 35.61452,
        "lon": -88.81395,
        "name": "Jackson"
      },
      {
        "lat": 34.02316,
        "lon": -84.36159,
        "name": "Roswell"
      },
      {
        "lat": 38.92567,
        "lon": -77.02942,
        "name": "Columbia Heights"
      },
      {
        "lat": 40.8601,
        "lon": -73.9093,
        "name": "University Heights"
      },
      {
        "lat": 28.54944,
        "lon": -81.77285,
        "name": "Clermont"
      }
    ],
    "ground_truth": {
      "area_km2": 1272916.78,
      "perimeter_km": 6685.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Frontera: (18.5433°, -92.6453°)",
      "  Jackson: (35.6145°, -88.8140°)",
      "  Roswell: (34.0232°, -84.3616°)",
      "  Columbia Heights: (38.9257°, -77.0294°)",
      "  University Heights: (40.8601°, -73.9093°)",
      "  Clermont: (28.5494°, -81.7729°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6685.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1272916.78 km²",
      "FINAL ANSWER: Area: 1272916.78 km², Perimeter: 6685.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 16.36554,
        "lon": -92.37063,
        "name": "Las Rosas"
      },
      {
        "lat": 38.83494,
        "lon": -90.28511,
        "name": "Old Jamestown"
      },
      {
        "lat": 33.88399,
        "lon": -84.51438,
        "name": "Smyrna"
      },
      {
        "lat": 23.0881,
        "lon": -82.3597,
        "name": "Diez de Octubre"
      }
    ],
    "ground_truth": {
      "area_km2": 1453148.64,
      "perimeter_km": 5766.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Las Rosas: (16.3655°, -92.3706°)",
      "  Old Jamestown: (38.8349°, -90.2851°)",
      "  Smyrna: (33.8840°, -84.5144°)",
      "  Diez de Octubre: (23.0881°, -82.3597°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5766.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1453148.64 km²",
      "FINAL ANSWER: Area: 1453148.64 km², Perimeter: 5766.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 29.61972,
        "lon": 31.2575,
        "name": "Al ‘Ayyāţ"
      },
      {
        "lat": 30.22886,
        "lon": 31.48149,
        "name": "Al-'Ubūr"
      },
      {
        "lat": 31.20864,
        "lon": 31.63528,
        "name": "Az Zarqā"
      },
      {
        "lat": 14.03493,
        "lon": 35.38344,
        "name": "Al Qadarif"
      },
      {
        "lat": 17.59898,
        "lon": 33.97205,
        "name": "Ed Damer"
      },
      {
        "lat": 16.6915,
        "lon": 33.4341,
        "name": "Shendi"
      }
    ],
    "ground_truth": {
      "area_km2": 174115.11,
      "perimeter_km": 4123.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Al ‘Ayyāţ: (29.6197°, 31.2575°)",
      "  Al-'Ubūr: (30.2289°, 31.4815°)",
      "  Az Zarqā: (31.2086°, 31.6353°)",
      "  Al Qadarif: (14.0349°, 35.3834°)",
      "  Ed Damer: (17.5990°, 33.9721°)",
      "  Shendi: (16.6915°, 33.4341°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4123.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 174115.11 km²",
      "FINAL ANSWER: Area: 174115.11 km², Perimeter: 4123.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 14.2277,
        "lon": 121.3292,
        "name": "Victoria"
      },
      {
        "lat": 24.07327,
        "lon": 120.56276,
        "name": "Chang-hua"
      },
      {
        "lat": 26.37609,
        "lon": 127.85908,
        "name": "Uruma"
      },
      {
        "lat": 5.82417,
        "lon": 125.20333,
        "name": "Glan"
      }
    ],
    "ground_truth": {
      "area_km2": 1017315.13,
      "perimeter_km": 5203.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Victoria: (14.2277°, 121.3292°)",
      "  Chang-hua: (24.0733°, 120.5628°)",
      "  Uruma: (26.3761°, 127.8591°)",
      "  Glan: (5.8242°, 125.2033°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5203.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1017315.13 km²",
      "FINAL ANSWER: Area: 1017315.13 km², Perimeter: 5203.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.13333,
        "lon": 145.13333,
        "name": "Frankston East"
      },
      {
        "lat": -37.66667,
        "lon": 145.01667,
        "name": "Lalor"
      },
      {
        "lat": -28.21901,
        "lon": 152.03438,
        "name": "Warwick"
      },
      {
        "lat": -28.11694,
        "lon": 153.46584,
        "name": "Palm Beach"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.85,
        "lon": 151.03333,
        "name": "Auburn"
      }
    ],
    "ground_truth": {
      "area_km2": 214589.53,
      "perimeter_km": 2826.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Frankston East: (-38.1333°, 145.1333°)",
      "  Lalor: (-37.6667°, 145.0167°)",
      "  Warwick: (-28.2190°, 152.0344°)",
      "  Palm Beach: (-28.1169°, 153.4658°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Auburn: (-33.8500°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2826.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 214589.53 km²",
      "FINAL ANSWER: Area: 214589.53 km², Perimeter: 2826.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.78247,
        "lon": 145.31682,
        "name": "Mooroolbark"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -27.87683,
        "lon": 153.28572,
        "name": "Upper Coomera"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.73333,
        "lon": 151.0,
        "name": "Castle Hill"
      }
    ],
    "ground_truth": {
      "area_km2": 165484.76,
      "perimeter_km": 2865.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mooroolbark: (-37.7825°, 145.3168°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Upper Coomera: (-27.8768°, 153.2857°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Castle Hill: (-33.7333°, 151.0000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2865.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 165484.76 km²",
      "FINAL ANSWER: Area: 165484.76 km², Perimeter: 2865.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 29.20856,
        "lon": 105.56974,
        "name": "Xuantan"
      },
      {
        "lat": 29.71975,
        "lon": 106.72342,
        "name": "Yufengshan"
      },
      {
        "lat": 32.23341,
        "lon": 106.30126,
        "name": "Donghe"
      },
      {
        "lat": 38.41667,
        "lon": 126.23333,
        "name": "Sinmak"
      },
      {
        "lat": 31.37762,
        "lon": 120.95431,
        "name": "Kunshan"
      }
    ],
    "ground_truth": {
      "area_km2": 845297.78,
      "perimeter_km": 4751.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Xuantan: (29.2086°, 105.5697°)",
      "  Yufengshan: (29.7198°, 106.7234°)",
      "  Donghe: (32.2334°, 106.3013°)",
      "  Sinmak: (38.4167°, 126.2333°)",
      "  Kunshan: (31.3776°, 120.9543°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4751.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 845297.78 km²",
      "FINAL ANSWER: Area: 845297.78 km², Perimeter: 4751.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.43884,
        "lon": 2.16893,
        "name": "la Guineueta"
      },
      {
        "lat": 48.8262,
        "lon": 2.35986,
        "name": "Paris 13e Arrondissement"
      },
      {
        "lat": 53.22683,
        "lon": -0.53792,
        "name": "Lincoln"
      },
      {
        "lat": 50.58362,
        "lon": 5.50115,
        "name": "Seraing"
      },
      {
        "lat": 51.51312,
        "lon": 10.25951,
        "name": "Duderstadt"
      },
      {
        "lat": 45.95689,
        "lon": 12.66051,
        "name": "Pordenone"
      }
    ],
    "ground_truth": {
      "area_km2": 790990.0,
      "perimeter_km": 3829.91,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  la Guineueta: (41.4388°, 2.1689°)",
      "  Paris 13e Arrondissement: (48.8262°, 2.3599°)",
      "  Lincoln: (53.2268°, -0.5379°)",
      "  Seraing: (50.5836°, 5.5011°)",
      "  Duderstadt: (51.5131°, 10.2595°)",
      "  Pordenone: (45.9569°, 12.6605°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3829.91 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 790990.00 km²",
      "FINAL ANSWER: Area: 790990.00 km², Perimeter: 3829.91 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.06022,
        "lon": -111.97105,
        "name": "Layton"
      },
      {
        "lat": 41.13998,
        "lon": -104.82025,
        "name": "Cheyenne"
      },
      {
        "lat": 41.81392,
        "lon": -87.61727,
        "name": "Grand Boulevard"
      },
      {
        "lat": 33.61983,
        "lon": -86.60888,
        "name": "Trussville"
      }
    ],
    "ground_truth": {
      "area_km2": 995898.64,
      "perimeter_km": 5326.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Layton: (41.0602°, -111.9711°)",
      "  Cheyenne: (41.1400°, -104.8203°)",
      "  Grand Boulevard: (41.8139°, -87.6173°)",
      "  Trussville: (33.6198°, -86.6089°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5326.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 995898.64 km²",
      "FINAL ANSWER: Area: 995898.64 km², Perimeter: 5326.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 17.64344,
        "lon": -101.55212,
        "name": "Ixtapa-Zihuatanejo"
      },
      {
        "lat": 32.85791,
        "lon": -97.25474,
        "name": "Watauga"
      },
      {
        "lat": 13.66492,
        "lon": -89.25319,
        "name": "Antiguo Cuscatlán"
      }
    ],
    "ground_truth": {
      "area_km2": 1223386.67,
      "perimeter_km": 5417.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ixtapa-Zihuatanejo: (17.6434°, -101.5521°)",
      "  Watauga: (32.8579°, -97.2547°)",
      "  Antiguo Cuscatlán: (13.6649°, -89.2532°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5417.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1223386.67 km²",
      "FINAL ANSWER: Area: 1223386.67 km², Perimeter: 5417.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.83242,
        "lon": -115.76312,
        "name": "Elko"
      },
      {
        "lat": 48.23251,
        "lon": -101.29627,
        "name": "Minot"
      },
      {
        "lat": 40.5142,
        "lon": -88.99063,
        "name": "Normal"
      },
      {
        "lat": 35.91537,
        "lon": -94.96996,
        "name": "Tahlequah"
      },
      {
        "lat": 32.58847,
        "lon": -96.95612,
        "name": "Cedar Hill"
      }
    ],
    "ground_truth": {
      "area_km2": 1896841.93,
      "perimeter_km": 5754.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Elko: (40.8324°, -115.7631°)",
      "  Minot: (48.2325°, -101.2963°)",
      "  Normal: (40.5142°, -88.9906°)",
      "  Tahlequah: (35.9154°, -94.9700°)",
      "  Cedar Hill: (32.5885°, -96.9561°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5754.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1896841.93 km²",
      "FINAL ANSWER: Area: 1896841.93 km², Perimeter: 5754.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -30.08389,
        "lon": -51.61611,
        "name": "Eldorado do Sul"
      },
      {
        "lat": -23.13705,
        "lon": -64.32426,
        "name": "San Ramón de la Nueva Orán"
      },
      {
        "lat": -18.59222,
        "lon": -48.705,
        "name": "Tupaciguara"
      },
      {
        "lat": -21.97722,
        "lon": -44.9325,
        "name": "Caxambu"
      },
      {
        "lat": -23.54667,
        "lon": -47.43778,
        "name": "Votorantim"
      },
      {
        "lat": -26.23,
        "lon": -51.08639,
        "name": "União da Vitória"
      }
    ],
    "ground_truth": {
      "area_km2": 1378083.41,
      "perimeter_km": 4938.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Eldorado do Sul: (-30.0839°, -51.6161°)",
      "  San Ramón de la Nueva Orán: (-23.1370°, -64.3243°)",
      "  Tupaciguara: (-18.5922°, -48.7050°)",
      "  Caxambu: (-21.9772°, -44.9325°)",
      "  Votorantim: (-23.5467°, -47.4378°)",
      "  União da Vitória: (-26.2300°, -51.0864°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4938.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1378083.41 km²",
      "FINAL ANSWER: Area: 1378083.41 km², Perimeter: 4938.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 44.4196,
        "lon": 27.82536,
        "name": "Fetești-Gară"
      },
      {
        "lat": 55.83333,
        "lon": 37.66667,
        "name": "Rostokino"
      },
      {
        "lat": 50.19645,
        "lon": 39.56631,
        "name": "Rossosh’"
      },
      {
        "lat": 43.24206,
        "lon": 46.00013,
        "name": "Tsotsin-Yurt"
      }
    ],
    "ground_truth": {
      "area_km2": 828686.46,
      "perimeter_km": 4462.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Fetești-Gară: (44.4196°, 27.8254°)",
      "  Rostokino: (55.8333°, 37.6667°)",
      "  Rossosh’: (50.1964°, 39.5663°)",
      "  Tsotsin-Yurt: (43.2421°, 46.0001°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4462.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 828686.46 km²",
      "FINAL ANSWER: Area: 828686.46 km², Perimeter: 4462.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -20.03833,
        "lon": -47.74694,
        "name": "Igarapava"
      },
      {
        "lat": -23.44361,
        "lon": -51.87389,
        "name": "Sarandi"
      },
      {
        "lat": -3.72667,
        "lon": -44.22333,
        "name": "Pirapemas"
      },
      {
        "lat": -4.25667,
        "lon": -43.01278,
        "name": "Coelho Neto"
      },
      {
        "lat": -20.41278,
        "lon": -40.68306,
        "name": "Marechal Floriano"
      }
    ],
    "ground_truth": {
      "area_km2": 1106000.54,
      "perimeter_km": 5610.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Igarapava: (-20.0383°, -47.7469°)",
      "  Sarandi: (-23.4436°, -51.8739°)",
      "  Pirapemas: (-3.7267°, -44.2233°)",
      "  Coelho Neto: (-4.2567°, -43.0128°)",
      "  Marechal Floriano: (-20.4128°, -40.6831°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5610.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1106000.54 km²",
      "FINAL ANSWER: Area: 1106000.54 km², Perimeter: 5610.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.27639,
        "lon": 35.59938,
        "name": "Kurayyimah"
      },
      {
        "lat": 32.67597,
        "lon": 35.23986,
        "name": "Migdal Ha‘Emeq"
      },
      {
        "lat": 41.5098,
        "lon": 34.21414,
        "name": "Taşköprü"
      },
      {
        "lat": 39.79803,
        "lon": 42.67574,
        "name": "Eleşkirt"
      },
      {
        "lat": 36.84722,
        "lon": 40.05,
        "name": "Ceylanpınar"
      }
    ],
    "ground_truth": {
      "area_km2": 388858.99,
      "perimeter_km": 2832.04,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kurayyimah: (32.2764°, 35.5994°)",
      "  Migdal Ha‘Emeq: (32.6760°, 35.2399°)",
      "  Taşköprü: (41.5098°, 34.2141°)",
      "  Eleşkirt: (39.7980°, 42.6757°)",
      "  Ceylanpınar: (36.8472°, 40.0500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2832.04 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 388858.99 km²",
      "FINAL ANSWER: Area: 388858.99 km², Perimeter: 2832.04 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.65071,
        "lon": -78.45639,
        "name": "Clayton"
      },
      {
        "lat": 42.90725,
        "lon": -85.79198,
        "name": "Jenison"
      },
      {
        "lat": 45.3001,
        "lon": -75.91606,
        "name": "Kanata"
      },
      {
        "lat": 42.27926,
        "lon": -71.1495,
        "name": "West Roxbury"
      },
      {
        "lat": 40.70038,
        "lon": -73.59291,
        "name": "Uniondale"
      }
    ],
    "ground_truth": {
      "area_km2": 668192.35,
      "perimeter_km": 3337.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Clayton: (35.6507°, -78.4564°)",
      "  Jenison: (42.9072°, -85.7920°)",
      "  Kanata: (45.3001°, -75.9161°)",
      "  West Roxbury: (42.2793°, -71.1495°)",
      "  Uniondale: (40.7004°, -73.5929°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3337.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 668192.35 km²",
      "FINAL ANSWER: Area: 668192.35 km², Perimeter: 3337.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.77988,
        "lon": 144.92276,
        "name": "Ascot Vale"
      },
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      },
      {
        "lat": -34.424,
        "lon": 150.89345,
        "name": "Wollongong"
      }
    ],
    "ground_truth": {
      "area_km2": 268476.14,
      "perimeter_km": 2498.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ascot Vale: (-37.7799°, 144.9228°)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "  Wollongong: (-34.4240°, 150.8935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2498.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 268476.14 km²",
      "FINAL ANSWER: Area: 268476.14 km², Perimeter: 2498.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 46.05223,
        "lon": 125.9552,
        "name": "Zhaodong"
      },
      {
        "lat": 46.97544,
        "lon": 128.04804,
        "name": "Tieli"
      },
      {
        "lat": 33.7,
        "lon": 135.41667,
        "name": "Asso"
      },
      {
        "lat": 31.34689,
        "lon": 130.45612,
        "name": "Minamikyushu"
      }
    ],
    "ground_truth": {
      "area_km2": 578858.04,
      "perimeter_km": 4005.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Zhaodong: (46.0522°, 125.9552°)",
      "  Tieli: (46.9754°, 128.0480°)",
      "  Asso: (33.7000°, 135.4167°)",
      "  Minamikyushu: (31.3469°, 130.4561°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4005.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 578858.04 km²",
      "FINAL ANSWER: Area: 578858.04 km², Perimeter: 4005.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.87693,
        "lon": -10.04964,
        "name": "Buchanan"
      },
      {
        "lat": 13.41033,
        "lon": -16.70815,
        "name": "Sukuta"
      },
      {
        "lat": 14.51255,
        "lon": -17.00447,
        "name": "Nguékhokh"
      },
      {
        "lat": 7.80335,
        "lon": -3.16832,
        "name": "Tanda"
      },
      {
        "lat": 7.69385,
        "lon": -5.03031,
        "name": "Bouaké"
      },
      {
        "lat": 5.69775,
        "lon": -0.32824,
        "name": "Atsiaman"
      }
    ],
    "ground_truth": {
      "area_km2": 614137.52,
      "perimeter_km": 4765.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Buchanan: (5.8769°, -10.0496°)",
      "  Sukuta: (13.4103°, -16.7081°)",
      "  Nguékhokh: (14.5125°, -17.0045°)",
      "  Tanda: (7.8034°, -3.1683°)",
      "  Bouaké: (7.6939°, -5.0303°)",
      "  Atsiaman: (5.6978°, -0.3282°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4765.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 614137.52 km²",
      "FINAL ANSWER: Area: 614137.52 km², Perimeter: 4765.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.8,
        "lon": 4.26667,
        "name": "Timizart"
      },
      {
        "lat": 36.772,
        "lon": 5.8982,
        "name": "District of Taher"
      },
      {
        "lat": 35.40417,
        "lon": 8.12417,
        "name": "Tébessa"
      },
      {
        "lat": 32.88743,
        "lon": 13.18733,
        "name": "Tripoli"
      },
      {
        "lat": 34.94529,
        "lon": 8.56789,
        "name": "Feriana"
      }
    ],
    "ground_truth": {
      "area_km2": 22537.88,
      "perimeter_km": 1862.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Timizart: (36.8000°, 4.2667°)",
      "  District of Taher: (36.7720°, 5.8982°)",
      "  Tébessa: (35.4042°, 8.1242°)",
      "  Tripoli: (32.8874°, 13.1873°)",
      "  Feriana: (34.9453°, 8.5679°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1862.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 22537.88 km²",
      "FINAL ANSWER: Area: 22537.88 km², Perimeter: 1862.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -21.72444,
        "lon": -48.10167,
        "name": "Américo Brasiliense"
      },
      {
        "lat": -8.49694,
        "lon": -36.94083,
        "name": "Pedra"
      },
      {
        "lat": -9.00972,
        "lon": -36.05833,
        "name": "São José da Laje"
      }
    ],
    "ground_truth": {
      "area_km2": 106530.27,
      "perimeter_km": 3919.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Américo Brasiliense: (-21.7244°, -48.1017°)",
      "  Pedra: (-8.4969°, -36.9408°)",
      "  São José da Laje: (-9.0097°, -36.0583°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3919.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 106530.27 km²",
      "FINAL ANSWER: Area: 106530.27 km², Perimeter: 3919.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -19.96778,
        "lon": -44.19833,
        "name": "Betim"
      },
      {
        "lat": -15.84577,
        "lon": -47.88369,
        "name": "Lago Sul"
      },
      {
        "lat": -3.36139,
        "lon": -42.41778,
        "name": "São Bernardo"
      },
      {
        "lat": -5.115,
        "lon": -36.63444,
        "name": "Macau"
      },
      {
        "lat": -7.73667,
        "lon": -37.99333,
        "name": "Princesa Isabel"
      }
    ],
    "ground_truth": {
      "area_km2": 1032953.14,
      "perimeter_km": 4626.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Betim: (-19.9678°, -44.1983°)",
      "  Lago Sul: (-15.8458°, -47.8837°)",
      "  São Bernardo: (-3.3614°, -42.4178°)",
      "  Macau: (-5.1150°, -36.6344°)",
      "  Princesa Isabel: (-7.7367°, -37.9933°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4626.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1032953.14 km²",
      "FINAL ANSWER: Area: 1032953.14 km², Perimeter: 4626.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -29.02889,
        "lon": -51.18167,
        "name": "Flores da Cunha"
      },
      {
        "lat": -25.78389,
        "lon": -53.30861,
        "name": "Salto do Lontra"
      },
      {
        "lat": -22.0175,
        "lon": -47.89083,
        "name": "São Carlos"
      }
    ],
    "ground_truth": {
      "area_km2": 143702.31,
      "perimeter_km": 1955.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Flores da Cunha: (-29.0289°, -51.1817°)",
      "  Salto do Lontra: (-25.7839°, -53.3086°)",
      "  São Carlos: (-22.0175°, -47.8908°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1955.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 143702.31 km²",
      "FINAL ANSWER: Area: 143702.31 km², Perimeter: 1955.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 29.2331,
        "lon": 56.6022,
        "name": "Bāft"
      },
      {
        "lat": 29.45137,
        "lon": 55.6809,
        "name": "Sirjan"
      },
      {
        "lat": 26.02401,
        "lon": 75.48182,
        "name": "Todaraisingh"
      }
    ],
    "ground_truth": {
      "area_km2": 13927.14,
      "perimeter_km": 3967.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bāft: (29.2331°, 56.6022°)",
      "  Sirjan: (29.4514°, 55.6809°)",
      "  Todaraisingh: (26.0240°, 75.4818°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3967.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13927.14 km²",
      "FINAL ANSWER: Area: 13927.14 km², Perimeter: 3967.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.32686,
        "lon": -2.98884,
        "name": "Leioa"
      },
      {
        "lat": 42.68607,
        "lon": 26.32558,
        "name": "Sliven"
      },
      {
        "lat": 42.67272,
        "lon": 21.16688,
        "name": "Pristina"
      }
    ],
    "ground_truth": {
      "area_km2": 89459.03,
      "perimeter_km": 4753.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Leioa: (43.3269°, -2.9888°)",
      "  Sliven: (42.6861°, 26.3256°)",
      "  Pristina: (42.6727°, 21.1669°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4753.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 89459.03 km²",
      "FINAL ANSWER: Area: 89459.03 km², Perimeter: 4753.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 8.322,
        "lon": 77.57711,
        "name": "Pānakkudi"
      },
      {
        "lat": 24.93805,
        "lon": 73.82392,
        "name": "Nāthdwāra"
      },
      {
        "lat": 18.8563,
        "lon": 82.5716,
        "name": "Jeypore"
      }
    ],
    "ground_truth": {
      "area_km2": 713662.81,
      "perimeter_km": 4306.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Pānakkudi: (8.3220°, 77.5771°)",
      "  Nāthdwāra: (24.9381°, 73.8239°)",
      "  Jeypore: (18.8563°, 82.5716°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4306.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 713662.81 km²",
      "FINAL ANSWER: Area: 713662.81 km², Perimeter: 4306.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -27.20338,
        "lon": 152.95923,
        "name": "Narangba"
      },
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      }
    ],
    "ground_truth": {
      "area_km2": 738287.89,
      "perimeter_km": 4216.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Narangba: (-27.2034°, 152.9592°)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4216.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 738287.89 km²",
      "FINAL ANSWER: Area: 738287.89 km², Perimeter: 4216.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.97647,
        "lon": -7.79834,
        "name": "Zou"
      },
      {
        "lat": 12.81028,
        "lon": -16.22639,
        "name": "Bignona"
      },
      {
        "lat": 8.939,
        "lon": 4.78227,
        "name": "Bode Saadu"
      }
    ],
    "ground_truth": {
      "area_km2": 572294.01,
      "perimeter_km": 4863.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Zou: (6.9765°, -7.7983°)",
      "  Bignona: (12.8103°, -16.2264°)",
      "  Bode Saadu: (8.9390°, 4.7823°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4863.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 572294.01 km²",
      "FINAL ANSWER: Area: 572294.01 km², Perimeter: 4863.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 0.4,
        "lon": 32.63333,
        "name": "Kira"
      },
      {
        "lat": 7.70111,
        "lon": 27.98972,
        "name": "Wau"
      },
      {
        "lat": 9.08569,
        "lon": 40.86708,
        "name": "Āsbe Teferī"
      }
    ],
    "ground_truth": {
      "area_km2": 619752.36,
      "perimeter_km": 3714.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Kira: (0.4000°, 32.6333°)",
      "  Wau: (7.7011°, 27.9897°)",
      "  Āsbe Teferī: (9.0857°, 40.8671°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3714.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 619752.36 km²",
      "FINAL ANSWER: Area: 619752.36 km², Perimeter: 3714.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -16.92366,
        "lon": 145.76613,
        "name": "Cairns"
      },
      {
        "lat": -27.19354,
        "lon": 153.02631,
        "name": "Deception Bay"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -33.79068,
        "lon": 150.6693,
        "name": "Glenmore Park"
      }
    ],
    "ground_truth": {
      "area_km2": 533018.95,
      "perimeter_km": 4141.48,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Cairns: (-16.9237°, 145.7661°)",
      "  Deception Bay: (-27.1935°, 153.0263°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Glenmore Park: (-33.7907°, 150.6693°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4141.48 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 533018.95 km²",
      "FINAL ANSWER: Area: 533018.95 km², Perimeter: 4141.48 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.31811,
        "lon": 114.26994,
        "name": "Hang Hau"
      },
      {
        "lat": 35.0616,
        "lon": 105.79108,
        "name": "Lianhua"
      },
      {
        "lat": 32.77856,
        "lon": 130.74537,
        "name": "Kotō"
      },
      {
        "lat": 23.95671,
        "lon": 120.57608,
        "name": "Yuanlin"
      }
    ],
    "ground_truth": {
      "area_km2": 1872788.96,
      "perimeter_km": 6015.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hang Hau: (22.3181°, 114.2699°)",
      "  Lianhua: (35.0616°, 105.7911°)",
      "  Kotō: (32.7786°, 130.7454°)",
      "  Yuanlin: (23.9567°, 120.5761°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6015.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1872788.96 km²",
      "FINAL ANSWER: Area: 1872788.96 km², Perimeter: 6015.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 44.84963,
        "lon": 7.72032,
        "name": "Carmagnola"
      },
      {
        "lat": 48.77334,
        "lon": 2.07393,
        "name": "Guyancourt"
      },
      {
        "lat": 53.36592,
        "lon": -1.99986,
        "name": "New Mills"
      },
      {
        "lat": 51.38707,
        "lon": 7.77019,
        "name": "Hemer"
      },
      {
        "lat": 53.944,
        "lon": 27.7823,
        "name": "Kalodzishchy"
      },
      {
        "lat": 40.5825,
        "lon": 22.95028,
        "name": "Kalamariá"
      }
    ],
    "ground_truth": {
      "area_km2": 1758996.14,
      "perimeter_km": 6126.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Carmagnola: (44.8496°, 7.7203°)",
      "  Guyancourt: (48.7733°, 2.0739°)",
      "  New Mills: (53.3659°, -1.9999°)",
      "  Hemer: (51.3871°, 7.7702°)",
      "  Kalodzishchy: (53.9440°, 27.7823°)",
      "  Kalamariá: (40.5825°, 22.9503°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6126.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1758996.14 km²",
      "FINAL ANSWER: Area: 1758996.14 km², Perimeter: 6126.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.52336,
        "lon": 119.51009,
        "name": "Heshan"
      },
      {
        "lat": 45.54558,
        "lon": 126.95191,
        "name": "Acheng"
      },
      {
        "lat": 36.71667,
        "lon": 139.68333,
        "name": "Imaichi"
      },
      {
        "lat": 36.76835,
        "lon": 137.12572,
        "name": "Imizu"
      },
      {
        "lat": 35.35043,
        "lon": 139.87029,
        "name": "Kimitsu"
      }
    ],
    "ground_truth": {
      "area_km2": 1048061.97,
      "perimeter_km": 5086.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Heshan: (35.5234°, 119.5101°)",
      "  Acheng: (45.5456°, 126.9519°)",
      "  Imaichi: (36.7167°, 139.6833°)",
      "  Imizu: (36.7683°, 137.1257°)",
      "  Kimitsu: (35.3504°, 139.8703°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5086.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1048061.97 km²",
      "FINAL ANSWER: Area: 1048061.97 km², Perimeter: 5086.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.20005,
        "lon": -86.51861,
        "name": "Mount Juliet"
      },
      {
        "lat": 42.16558,
        "lon": -88.29425,
        "name": "Algonquin"
      },
      {
        "lat": 42.81424,
        "lon": -73.93957,
        "name": "Schenectady"
      },
      {
        "lat": 42.00288,
        "lon": -71.51478,
        "name": "Woonsocket"
      },
      {
        "lat": 40.02789,
        "lon": -74.86905,
        "name": "Willingboro"
      }
    ],
    "ground_truth": {
      "area_km2": 583811.39,
      "perimeter_km": 3537.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mount Juliet: (36.2000°, -86.5186°)",
      "  Algonquin: (42.1656°, -88.2943°)",
      "  Schenectady: (42.8142°, -73.9396°)",
      "  Woonsocket: (42.0029°, -71.5148°)",
      "  Willingboro: (40.0279°, -74.8691°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3537.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 583811.39 km²",
      "FINAL ANSWER: Area: 583811.39 km², Perimeter: 3537.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.44363,
        "lon": -117.00371,
        "name": "La Joya"
      },
      {
        "lat": 33.9938,
        "lon": -117.75888,
        "name": "Chino Hills"
      },
      {
        "lat": 37.69465,
        "lon": -122.11385,
        "name": "Ashland"
      },
      {
        "lat": 49.24966,
        "lon": -123.11934,
        "name": "Vancouver"
      },
      {
        "lat": 40.56217,
        "lon": -111.92966,
        "name": "South Jordan"
      },
      {
        "lat": 32.89953,
        "lon": -105.96027,
        "name": "Alamogordo"
      }
    ],
    "ground_truth": {
      "area_km2": 1367150.65,
      "perimeter_km": 5385.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  La Joya: (32.4436°, -117.0037°)",
      "  Chino Hills: (33.9938°, -117.7589°)",
      "  Ashland: (37.6947°, -122.1138°)",
      "  Vancouver: (49.2497°, -123.1193°)",
      "  South Jordan: (40.5622°, -111.9297°)",
      "  Alamogordo: (32.8995°, -105.9603°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5385.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1367150.65 km²",
      "FINAL ANSWER: Area: 1367150.65 km², Perimeter: 5385.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.94203,
        "lon": 23.64619,
        "name": "Piraeus"
      },
      {
        "lat": 47.31667,
        "lon": 21.11667,
        "name": "Püspökladány"
      },
      {
        "lat": 55.75378,
        "lon": 37.81885,
        "name": "Novogireyevo"
      },
      {
        "lat": 48.02708,
        "lon": 40.12305,
        "name": "Zverevo"
      },
      {
        "lat": 45.09778,
        "lon": 43.43639,
        "name": "Blagodarnyy"
      },
      {
        "lat": 43.16345,
        "lon": 46.00152,
        "name": "Avtury"
      }
    ],
    "ground_truth": {
      "area_km2": 1972378.07,
      "perimeter_km": 6096.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Piraeus: (37.9420°, 23.6462°)",
      "  Püspökladány: (47.3167°, 21.1167°)",
      "  Novogireyevo: (55.7538°, 37.8188°)",
      "  Zverevo: (48.0271°, 40.1230°)",
      "  Blagodarnyy: (45.0978°, 43.4364°)",
      "  Avtury: (43.1634°, 46.0015°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6096.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1972378.07 km²",
      "FINAL ANSWER: Area: 1972378.07 km², Perimeter: 6096.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 18.15619,
        "lon": 83.44727,
        "name": "Nellimarla"
      },
      {
        "lat": 15.85212,
        "lon": 74.50447,
        "name": "Belagavi"
      },
      {
        "lat": 21.77369,
        "lon": 79.80513,
        "name": "Katangi"
      },
      {
        "lat": 24.39735,
        "lon": 98.5177,
        "name": "Fengping"
      }
    ],
    "ground_truth": {
      "area_km2": 696111.68,
      "perimeter_km": 5489.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Nellimarla: (18.1562°, 83.4473°)",
      "  Belagavi: (15.8521°, 74.5045°)",
      "  Katangi: (21.7737°, 79.8051°)",
      "  Fengping: (24.3973°, 98.5177°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5489.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 696111.68 km²",
      "FINAL ANSWER: Area: 696111.68 km², Perimeter: 5489.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 26.35869,
        "lon": -80.0831,
        "name": "Boca Raton"
      },
      {
        "lat": 28.88305,
        "lon": -81.30868,
        "name": "DeBary"
      },
      {
        "lat": 35.88264,
        "lon": -80.08199,
        "name": "Thomasville"
      },
      {
        "lat": 18.47116,
        "lon": -77.91883,
        "name": "Montego Bay"
      }
    ],
    "ground_truth": {
      "area_km2": 185732.82,
      "perimeter_km": 3944.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Boca Raton: (26.3587°, -80.0831°)",
      "  DeBary: (28.8831°, -81.3087°)",
      "  Thomasville: (35.8826°, -80.0820°)",
      "  Montego Bay: (18.4712°, -77.9188°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3944.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 185732.82 km²",
      "FINAL ANSWER: Area: 185732.82 km², Perimeter: 3944.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.11342,
        "lon": 145.28326,
        "name": "Cranbourne"
      },
      {
        "lat": -37.65,
        "lon": 145.03333,
        "name": "Epping"
      },
      {
        "lat": -27.50578,
        "lon": 153.10236,
        "name": "Carindale"
      },
      {
        "lat": -22.15757,
        "lon": 166.4572,
        "name": "Dumbéa"
      }
    ],
    "ground_truth": {
      "area_km2": 691939.66,
      "perimeter_km": 5572.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Cranbourne: (-38.1134°, 145.2833°)",
      "  Epping: (-37.6500°, 145.0333°)",
      "  Carindale: (-27.5058°, 153.1024°)",
      "  Dumbéa: (-22.1576°, 166.4572°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5572.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 691939.66 km²",
      "FINAL ANSWER: Area: 691939.66 km², Perimeter: 5572.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -5.08917,
        "lon": -81.11444,
        "name": "Paita"
      },
      {
        "lat": 6.34633,
        "lon": -75.50888,
        "name": "Copacabana"
      },
      {
        "lat": 0.87136,
        "lon": -77.64027,
        "name": "Pupiales"
      }
    ],
    "ground_truth": {
      "area_km2": 39376.45,
      "perimeter_km": 2835.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Paita: (-5.0892°, -81.1144°)",
      "  Copacabana: (6.3463°, -75.5089°)",
      "  Pupiales: (0.8714°, -77.6403°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2835.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 39376.45 km²",
      "FINAL ANSWER: Area: 39376.45 km², Perimeter: 2835.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.02639,
        "lon": -45.55528,
        "name": "Taubaté"
      },
      {
        "lat": -6.96596,
        "lon": -35.7951,
        "name": "Remígio"
      },
      {
        "lat": -8.75632,
        "lon": -35.09995,
        "name": "Tamandaré"
      }
    ],
    "ground_truth": {
      "area_km2": 170889.76,
      "perimeter_km": 4220.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Taubaté: (-23.0264°, -45.5553°)",
      "  Remígio: (-6.9660°, -35.7951°)",
      "  Tamandaré: (-8.7563°, -35.0999°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4220.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 170889.76 km²",
      "FINAL ANSWER: Area: 170889.76 km², Perimeter: 4220.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 11.46009,
        "lon": 78.18635,
        "name": "Rasipuram"
      },
      {
        "lat": 8.29957,
        "lon": 77.24062,
        "name": "Unnamalaikadai"
      },
      {
        "lat": 10.47327,
        "lon": 76.25577,
        "name": "Marattakara"
      },
      {
        "lat": 15.25612,
        "lon": 75.24735,
        "name": "Kundgol"
      },
      {
        "lat": 23.63722,
        "lon": 79.06275,
        "name": "Rehli"
      },
      {
        "lat": 23.62118,
        "lon": 85.46748,
        "name": "Barkā Kānā"
      }
    ],
    "ground_truth": {
      "area_km2": 769497.43,
      "perimeter_km": 4396.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Rasipuram: (11.4601°, 78.1864°)",
      "  Unnamalaikadai: (8.2996°, 77.2406°)",
      "  Marattakara: (10.4733°, 76.2558°)",
      "  Kundgol: (15.2561°, 75.2473°)",
      "  Rehli: (23.6372°, 79.0627°)",
      "  Barkā Kānā: (23.6212°, 85.4675°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4396.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 769497.43 km²",
      "FINAL ANSWER: Area: 769497.43 km², Perimeter: 4396.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.85262,
        "lon": -82.39401,
        "name": "Greenville"
      },
      {
        "lat": 40.94782,
        "lon": -90.37124,
        "name": "Galesburg"
      },
      {
        "lat": 40.78788,
        "lon": -74.01431,
        "name": "West New York"
      }
    ],
    "ground_truth": {
      "area_km2": 482566.48,
      "perimeter_km": 3334.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Greenville: (34.8526°, -82.3940°)",
      "  Galesburg: (40.9478°, -90.3712°)",
      "  West New York: (40.7879°, -74.0143°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3334.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 482566.48 km²",
      "FINAL ANSWER: Area: 482566.48 km², Perimeter: 3334.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -34.28853,
        "lon": 146.05093,
        "name": "Griffith"
      },
      {
        "lat": -31.9652,
        "lon": 141.4512,
        "name": "Broken Hill"
      },
      {
        "lat": -28.21298,
        "lon": 153.53634,
        "name": "Banora Point"
      },
      {
        "lat": -33.89743,
        "lon": 150.93446,
        "name": "Cabramatta"
      }
    ],
    "ground_truth": {
      "area_km2": 367552.59,
      "perimeter_km": 2865.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Griffith: (-34.2885°, 146.0509°)",
      "  Broken Hill: (-31.9652°, 141.4512°)",
      "  Banora Point: (-28.2130°, 153.5363°)",
      "  Cabramatta: (-33.8974°, 150.9345°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2865.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 367552.59 km²",
      "FINAL ANSWER: Area: 367552.59 km², Perimeter: 2865.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.61162,
        "lon": -119.52707,
        "name": "Parlier"
      },
      {
        "lat": 36.97412,
        "lon": -122.0308,
        "name": "Santa Cruz"
      },
      {
        "lat": 47.18538,
        "lon": -122.2929,
        "name": "Puyallup"
      },
      {
        "lat": 50.28337,
        "lon": -107.80135,
        "name": "Swift Current"
      },
      {
        "lat": 40.31412,
        "lon": -112.00688,
        "name": "Eagle Mountain"
      }
    ],
    "ground_truth": {
      "area_km2": 1105498.58,
      "perimeter_km": 4406.11,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Parlier: (36.6116°, -119.5271°)",
      "  Santa Cruz: (36.9741°, -122.0308°)",
      "  Puyallup: (47.1854°, -122.2929°)",
      "  Swift Current: (50.2834°, -107.8013°)",
      "  Eagle Mountain: (40.3141°, -112.0069°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4406.11 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1105498.58 km²",
      "FINAL ANSWER: Area: 1105498.58 km², Perimeter: 4406.11 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.92889,
        "lon": 116.46528,
        "name": "Yucheng"
      },
      {
        "lat": 40.32306,
        "lon": 128.65528,
        "name": "Iwŏn-ŭp"
      },
      {
        "lat": 35.91333,
        "lon": 128.82,
        "name": "Hayang"
      },
      {
        "lat": 32.65,
        "lon": 130.66667,
        "name": "Matsubase"
      }
    ],
    "ground_truth": {
      "area_km2": 483680.8,
      "perimeter_km": 3454.62,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Yucheng: (34.9289°, 116.4653°)",
      "  Iwŏn-ŭp: (40.3231°, 128.6553°)",
      "  Hayang: (35.9133°, 128.8200°)",
      "  Matsubase: (32.6500°, 130.6667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3454.62 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 483680.80 km²",
      "FINAL ANSWER: Area: 483680.80 km², Perimeter: 3454.62 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 8.54884,
        "lon": 76.91716,
        "name": "Sreekaryam"
      },
      {
        "lat": 23.84765,
        "lon": 78.79903,
        "name": "Makronia"
      },
      {
        "lat": 13.21055,
        "lon": 79.0956,
        "name": "Chittoor"
      },
      {
        "lat": 10.92687,
        "lon": 79.27056,
        "name": "Papanasam"
      }
    ],
    "ground_truth": {
      "area_km2": 186154.96,
      "perimeter_km": 3520.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sreekaryam: (8.5488°, 76.9172°)",
      "  Makronia: (23.8477°, 78.7990°)",
      "  Chittoor: (13.2105°, 79.0956°)",
      "  Papanasam: (10.9269°, 79.2706°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3520.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 186154.96 km²",
      "FINAL ANSWER: Area: 186154.96 km², Perimeter: 3520.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -12.05048,
        "lon": -76.97335,
        "name": "Santa Anita - Los Ficus"
      },
      {
        "lat": -7.05614,
        "lon": -76.5911,
        "name": "Bellavista"
      },
      {
        "lat": -17.39228,
        "lon": -66.27838,
        "name": "Quillacollo"
      },
      {
        "lat": -20.21326,
        "lon": -70.15027,
        "name": "Iquique"
      }
    ],
    "ground_truth": {
      "area_km2": 630329.33,
      "perimeter_km": 3838.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Santa Anita - Los Ficus: (-12.0505°, -76.9733°)",
      "  Bellavista: (-7.0561°, -76.5911°)",
      "  Quillacollo: (-17.3923°, -66.2784°)",
      "  Iquique: (-20.2133°, -70.1503°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3838.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 630329.33 km²",
      "FINAL ANSWER: Area: 630329.33 km², Perimeter: 3838.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 0.60419,
        "lon": 29.31004,
        "name": "Mangina"
      },
      {
        "lat": 3.03716,
        "lon": 29.53551,
        "name": "Watsa"
      },
      {
        "lat": 13.15611,
        "lon": 37.89806,
        "name": "Debark’"
      },
      {
        "lat": 8.66667,
        "lon": 38.21667,
        "name": "Tulu Bolo"
      }
    ],
    "ground_truth": {
      "area_km2": 374736.65,
      "perimeter_km": 3557.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mangina: (0.6042°, 29.3100°)",
      "  Watsa: (3.0372°, 29.5355°)",
      "  Debark’: (13.1561°, 37.8981°)",
      "  Tulu Bolo: (8.6667°, 38.2167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3557.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 374736.65 km²",
      "FINAL ANSWER: Area: 374736.65 km², Perimeter: 3557.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.01034,
        "lon": 34.77918,
        "name": "H̱olon"
      },
      {
        "lat": 31.58428,
        "lon": 54.4428,
        "name": "Mahrīz"
      },
      {
        "lat": 26.18872,
        "lon": 73.02649,
        "name": "Sāngaria"
      }
    ],
    "ground_truth": {
      "area_km2": 223374.9,
      "perimeter_km": 7511.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  H̱olon: (32.0103°, 34.7792°)",
      "  Mahrīz: (31.5843°, 54.4428°)",
      "  Sāngaria: (26.1887°, 73.0265°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7511.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 223374.90 km²",
      "FINAL ANSWER: Area: 223374.90 km², Perimeter: 7511.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.7688,
        "lon": -1.50229,
        "name": "Totana"
      },
      {
        "lat": 40.38897,
        "lon": -3.74569,
        "name": "Latina"
      },
      {
        "lat": 47.36667,
        "lon": 1.75,
        "name": "Romorantin-Lanthenay"
      },
      {
        "lat": 53.10766,
        "lon": 8.46322,
        "name": "Hude"
      },
      {
        "lat": 41.00996,
        "lon": 14.13013,
        "name": "Casal di Principe"
      }
    ],
    "ground_truth": {
      "area_km2": 1264334.99,
      "perimeter_km": 4837.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Totana: (37.7688°, -1.5023°)",
      "  Latina: (40.3890°, -3.7457°)",
      "  Romorantin-Lanthenay: (47.3667°, 1.7500°)",
      "  Hude: (53.1077°, 8.4632°)",
      "  Casal di Principe: (41.0100°, 14.1301°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4837.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1264334.99 km²",
      "FINAL ANSWER: Area: 1264334.99 km², Perimeter: 4837.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 0.69781,
        "lon": 29.51863,
        "name": "Hyosha"
      },
      {
        "lat": 7.31667,
        "lon": 38.08333,
        "name": "K’olīto"
      },
      {
        "lat": 6.8773,
        "lon": 37.93619,
        "name": "Badessa"
      }
    ],
    "ground_truth": {
      "area_km2": 17432.77,
      "perimeter_km": 2411.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hyosha: (0.6978°, 29.5186°)",
      "  K’olīto: (7.3167°, 38.0833°)",
      "  Badessa: (6.8773°, 37.9362°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2411.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 17432.77 km²",
      "FINAL ANSWER: Area: 17432.77 km², Perimeter: 2411.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -30.3875,
        "lon": -56.45139,
        "name": "Quaraí"
      },
      {
        "lat": -32.99835,
        "lon": -60.76791,
        "name": "Pérez"
      },
      {
        "lat": -16.03095,
        "lon": -48.02929,
        "name": "Santa Maria"
      },
      {
        "lat": -23.19361,
        "lon": -49.38389,
        "name": "Piraju"
      },
      {
        "lat": -28.65083,
        "lon": -49.21,
        "name": "Morro da Fumaça"
      },
      {
        "lat": -29.88667,
        "lon": -50.26972,
        "name": "Osório"
      }
    ],
    "ground_truth": {
      "area_km2": 644949.91,
      "perimeter_km": 4965.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Quaraí: (-30.3875°, -56.4514°)",
      "  Pérez: (-32.9984°, -60.7679°)",
      "  Santa Maria: (-16.0310°, -48.0293°)",
      "  Piraju: (-23.1936°, -49.3839°)",
      "  Morro da Fumaça: (-28.6508°, -49.2100°)",
      "  Osório: (-29.8867°, -50.2697°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4965.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 644949.91 km²",
      "FINAL ANSWER: Area: 644949.91 km², Perimeter: 4965.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.01223,
        "lon": -117.68894,
        "name": "Chino"
      },
      {
        "lat": 35.50672,
        "lon": -97.76254,
        "name": "Yukon"
      },
      {
        "lat": 30.51353,
        "lon": -97.73973,
        "name": "Brushy Creek"
      }
    ],
    "ground_truth": {
      "area_km2": 510382.16,
      "perimeter_km": 4292.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Chino: (34.0122°, -117.6889°)",
      "  Yukon: (35.5067°, -97.7625°)",
      "  Brushy Creek: (30.5135°, -97.7397°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4292.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 510382.16 km²",
      "FINAL ANSWER: Area: 510382.16 km², Perimeter: 4292.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.89138,
        "lon": 144.62368,
        "name": "Wyndham Vale"
      },
      {
        "lat": -20.72523,
        "lon": 139.49727,
        "name": "Mount Isa"
      },
      {
        "lat": -34.03857,
        "lon": 151.10005,
        "name": "Miranda"
      },
      {
        "lat": -37.97695,
        "lon": 145.25866,
        "name": "Endeavour Hills"
      }
    ],
    "ground_truth": {
      "area_km2": 694650.52,
      "perimeter_km": 4580.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wyndham Vale: (-37.8914°, 144.6237°)",
      "  Mount Isa: (-20.7252°, 139.4973°)",
      "  Miranda: (-34.0386°, 151.1001°)",
      "  Endeavour Hills: (-37.9770°, 145.2587°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4580.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 694650.52 km²",
      "FINAL ANSWER: Area: 694650.52 km², Perimeter: 4580.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 13.04394,
        "lon": 80.17251,
        "name": "Valasaravakkam"
      },
      {
        "lat": 15.78502,
        "lon": 80.30663,
        "name": "Vetapālem"
      },
      {
        "lat": 20.3306,
        "lon": 74.24467,
        "name": "Chāndor"
      },
      {
        "lat": 28.64133,
        "lon": 77.01415,
        "name": "Bāprola"
      },
      {
        "lat": 23.19259,
        "lon": 82.1272,
        "name": "Bangawan"
      },
      {
        "lat": 17.30132,
        "lon": 95.19833,
        "name": "Kyonpyaw"
      }
    ],
    "ground_truth": {
      "area_km2": 1710539.33,
      "perimeter_km": 6070.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Valasaravakkam: (13.0439°, 80.1725°)",
      "  Vetapālem: (15.7850°, 80.3066°)",
      "  Chāndor: (20.3306°, 74.2447°)",
      "  Bāprola: (28.6413°, 77.0142°)",
      "  Bangawan: (23.1926°, 82.1272°)",
      "  Kyonpyaw: (17.3013°, 95.1983°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6070.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1710539.33 km²",
      "FINAL ANSWER: Area: 1710539.33 km², Perimeter: 6070.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.814,
        "lon": 144.96332,
        "name": "Melbourne"
      },
      {
        "lat": -27.93994,
        "lon": 153.31436,
        "name": "Pacific Pines"
      },
      {
        "lat": -33.92893,
        "lon": 151.05111,
        "name": "Punchbowl"
      }
    ],
    "ground_truth": {
      "area_km2": 128116.72,
      "perimeter_km": 2743.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Melbourne: (-37.8140°, 144.9633°)",
      "  Pacific Pines: (-27.9399°, 153.3144°)",
      "  Punchbowl: (-33.9289°, 151.0511°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2743.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 128116.72 km²",
      "FINAL ANSWER: Area: 128116.72 km², Perimeter: 2743.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.54015,
        "lon": -46.48581,
        "name": "Artur Alvim"
      },
      {
        "lat": -16.3775,
        "lon": -39.58028,
        "name": "Eunápolis"
      },
      {
        "lat": -17.34111,
        "lon": -39.22083,
        "name": "Prado"
      }
    ],
    "ground_truth": {
      "area_km2": 53377.58,
      "perimeter_km": 2211.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Artur Alvim: (-23.5402°, -46.4858°)",
      "  Eunápolis: (-16.3775°, -39.5803°)",
      "  Prado: (-17.3411°, -39.2208°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2211.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 53377.58 km²",
      "FINAL ANSWER: Area: 53377.58 km², Perimeter: 2211.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 11.31823,
        "lon": -12.28332,
        "name": "Labé"
      },
      {
        "lat": 14.71542,
        "lon": -17.27334,
        "name": "Rufisque"
      },
      {
        "lat": 11.44379,
        "lon": -2.22548,
        "name": "Tô"
      },
      {
        "lat": 10.33137,
        "lon": -3.18202,
        "name": "Gaoua"
      }
    ],
    "ground_truth": {
      "area_km2": 288236.28,
      "perimeter_km": 3490.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Labé: (11.3182°, -12.2833°)",
      "  Rufisque: (14.7154°, -17.2733°)",
      "  Tô: (11.4438°, -2.2255°)",
      "  Gaoua: (10.3314°, -3.1820°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3490.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 288236.28 km²",
      "FINAL ANSWER: Area: 288236.28 km², Perimeter: 3490.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.32393,
        "lon": 5.4584,
        "name": "Les Olives"
      },
      {
        "lat": 47.49494,
        "lon": 8.71954,
        "name": "Stadt Winterthur (Kreis 1)"
      },
      {
        "lat": 51.81,
        "lon": 4.67361,
        "name": "Dordrecht"
      },
      {
        "lat": 41.76836,
        "lon": 26.19775,
        "name": "Svilengrad"
      },
      {
        "lat": 42.15387,
        "lon": 24.75001,
        "name": "Plovdiv"
      }
    ],
    "ground_truth": {
      "area_km2": 953618.99,
      "perimeter_km": 4765.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Les Olives: (43.3239°, 5.4584°)",
      "  Stadt Winterthur (Kreis 1): (47.4949°, 8.7195°)",
      "  Dordrecht: (51.8100°, 4.6736°)",
      "  Svilengrad: (41.7684°, 26.1977°)",
      "  Plovdiv: (42.1539°, 24.7500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4765.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 953618.99 km²",
      "FINAL ANSWER: Area: 953618.99 km², Perimeter: 4765.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.32124,
        "lon": 17.57461,
        "name": "Prudnik"
      },
      {
        "lat": 53.18478,
        "lon": -3.02578,
        "name": "Hawarden"
      },
      {
        "lat": 54.15,
        "lon": -4.48333,
        "name": "Douglas"
      },
      {
        "lat": 59.19858,
        "lon": 17.83317,
        "name": "Tumba"
      },
      {
        "lat": 57.87292,
        "lon": 39.52969,
        "name": "Tutayev"
      },
      {
        "lat": 48.17927,
        "lon": 40.7792,
        "name": "Belaya Kalitva"
      }
    ],
    "ground_truth": {
      "area_km2": 2264162.15,
      "perimeter_km": 7094.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Prudnik: (50.3212°, 17.5746°)",
      "  Hawarden: (53.1848°, -3.0258°)",
      "  Douglas: (54.1500°, -4.4833°)",
      "  Tumba: (59.1986°, 17.8332°)",
      "  Tutayev: (57.8729°, 39.5297°)",
      "  Belaya Kalitva: (48.1793°, 40.7792°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7094.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2264162.15 km²",
      "FINAL ANSWER: Area: 2264162.15 km², Perimeter: 7094.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.225,
        "lon": -123.0,
        "name": "Metrotown"
      },
      {
        "lat": 47.14121,
        "lon": -122.27012,
        "name": "South Hill"
      },
      {
        "lat": 38.66879,
        "lon": -120.98716,
        "name": "Cameron Park"
      }
    ],
    "ground_truth": {
      "area_km2": 12024.62,
      "perimeter_km": 2370.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Metrotown: (49.2250°, -123.0000°)",
      "  South Hill: (47.1412°, -122.2701°)",
      "  Cameron Park: (38.6688°, -120.9872°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2370.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 12024.62 km²",
      "FINAL ANSWER: Area: 12024.62 km², Perimeter: 2370.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.95889,
        "lon": -79.23917,
        "name": "Santiago de Cao"
      },
      {
        "lat": 6.17358,
        "lon": -75.33621,
        "name": "Marinilla"
      },
      {
        "lat": 9.31847,
        "lon": -75.2933,
        "name": "Corozal"
      },
      {
        "lat": -16.08333,
        "lon": -69.66667,
        "name": "Ilave"
      }
    ],
    "ground_truth": {
      "area_km2": 1284258.44,
      "perimeter_km": 6248.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Santiago de Cao: (-7.9589°, -79.2392°)",
      "  Marinilla: (6.1736°, -75.3362°)",
      "  Corozal: (9.3185°, -75.2933°)",
      "  Ilave: (-16.0833°, -69.6667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6248.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1284258.44 km²",
      "FINAL ANSWER: Area: 1284258.44 km², Perimeter: 6248.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -25.85583,
        "lon": -52.52333,
        "name": "Chopinzinho"
      },
      {
        "lat": -22.10809,
        "lon": -56.53253,
        "name": "Bela Vista"
      },
      {
        "lat": -22.90642,
        "lon": -43.18223,
        "name": "Rio de Janeiro"
      },
      {
        "lat": -23.63143,
        "lon": -46.62072,
        "name": "Cursino"
      },
      {
        "lat": -23.77806,
        "lon": -45.35806,
        "name": "Ilhabela"
      }
    ],
    "ground_truth": {
      "area_km2": 303501.86,
      "perimeter_km": 3205.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Chopinzinho: (-25.8558°, -52.5233°)",
      "  Bela Vista: (-22.1081°, -56.5325°)",
      "  Rio de Janeiro: (-22.9064°, -43.1822°)",
      "  Cursino: (-23.6314°, -46.6207°)",
      "  Ilhabela: (-23.7781°, -45.3581°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3205.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 303501.86 km²",
      "FINAL ANSWER: Area: 303501.86 km², Perimeter: 3205.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.32229,
        "lon": 19.07922,
        "name": "Dekoa"
      },
      {
        "lat": -1.09056,
        "lon": 29.2925,
        "name": "Kirumba"
      },
      {
        "lat": -2.07444,
        "lon": 29.75667,
        "name": "Gitarama"
      }
    ],
    "ground_truth": {
      "area_km2": 40800.63,
      "perimeter_km": 3031.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Dekoa: (6.3223°, 19.0792°)",
      "  Kirumba: (-1.0906°, 29.2925°)",
      "  Gitarama: (-2.0744°, 29.7567°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3031.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 40800.63 km²",
      "FINAL ANSWER: Area: 40800.63 km², Perimeter: 3031.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 36.20983,
        "lon": -5.38452,
        "name": "San Roque"
      },
      {
        "lat": 47.7996,
        "lon": 3.57033,
        "name": "Auxerre"
      },
      {
        "lat": 49.38167,
        "lon": 3.32361,
        "name": "Soissons"
      },
      {
        "lat": 52.225,
        "lon": 4.52222,
        "name": "Sassenheim"
      },
      {
        "lat": 57.81922,
        "lon": 28.33181,
        "name": "Pskov"
      },
      {
        "lat": 37.96775,
        "lon": 23.5721,
        "name": "Pérama"
      }
    ],
    "ground_truth": {
      "area_km2": 3918777.0,
      "perimeter_km": 8417.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  San Roque: (36.2098°, -5.3845°)",
      "  Auxerre: (47.7996°, 3.5703°)",
      "  Soissons: (49.3817°, 3.3236°)",
      "  Sassenheim: (52.2250°, 4.5222°)",
      "  Pskov: (57.8192°, 28.3318°)",
      "  Pérama: (37.9678°, 23.5721°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8417.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3918777.00 km²",
      "FINAL ANSWER: Area: 3918777.00 km², Perimeter: 8417.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.24467,
        "lon": 0.40418,
        "name": "Newmarket"
      },
      {
        "lat": 52.29083,
        "lon": 4.58333,
        "name": "Hillegom"
      },
      {
        "lat": 48.17319,
        "lon": 27.30075,
        "name": "Edineţ"
      }
    ],
    "ground_truth": {
      "area_km2": 25970.06,
      "perimeter_km": 3910.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Newmarket: (52.2447°, 0.4042°)",
      "  Hillegom: (52.2908°, 4.5833°)",
      "  Edineţ: (48.1732°, 27.3008°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3910.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 25970.06 km²",
      "FINAL ANSWER: Area: 25970.06 km², Perimeter: 3910.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -1.94995,
        "lon": 30.05885,
        "name": "Kigali"
      },
      {
        "lat": 1.15167,
        "lon": 33.155,
        "name": "Buyende"
      },
      {
        "lat": -3.13333,
        "lon": 33.53333,
        "name": "Malampaka"
      },
      {
        "lat": -8.9,
        "lon": 34.58333,
        "name": "Ilembula"
      },
      {
        "lat": -14.82027,
        "lon": 34.63586,
        "name": "Ntcheu"
      }
    ],
    "ground_truth": {
      "area_km2": 370425.97,
      "perimeter_km": 3792.3,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Kigali: (-1.9500°, 30.0588°)",
      "  Buyende: (1.1517°, 33.1550°)",
      "  Malampaka: (-3.1333°, 33.5333°)",
      "  Ilembula: (-8.9000°, 34.5833°)",
      "  Ntcheu: (-14.8203°, 34.6359°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3792.30 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 370425.97 km²",
      "FINAL ANSWER: Area: 370425.97 km², Perimeter: 3792.30 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -37.83382,
        "lon": 144.93834,
        "name": "City of Port Phillip"
      },
      {
        "lat": -27.62329,
        "lon": 153.04785,
        "name": "Calamvale"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -33.52314,
        "lon": 151.31325,
        "name": "Umina Beach"
      },
      {
        "lat": -33.94185,
        "lon": 150.8717,
        "name": "Prestons"
      }
    ],
    "ground_truth": {
      "area_km2": 214028.34,
      "perimeter_km": 2885.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  City of Port Phillip: (-37.8338°, 144.9383°)",
      "  Calamvale: (-27.6233°, 153.0479°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  Umina Beach: (-33.5231°, 151.3133°)",
      "  Prestons: (-33.9419°, 150.8717°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2885.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 214028.34 km²",
      "FINAL ANSWER: Area: 214028.34 km², Perimeter: 2885.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -30.71066,
        "lon": -62.00714,
        "name": "Morteros"
      },
      {
        "lat": -18.54389,
        "lon": -53.12917,
        "name": "Costa Rica"
      },
      {
        "lat": -13.03667,
        "lon": -46.77167,
        "name": "Campos Belos"
      },
      {
        "lat": -15.47949,
        "lon": -44.3652,
        "name": "Januária"
      },
      {
        "lat": -23.425,
        "lon": -49.72083,
        "name": "Carlópolis"
      }
    ],
    "ground_truth": {
      "area_km2": 959903.03,
      "perimeter_km": 5418.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Morteros: (-30.7107°, -62.0071°)",
      "  Costa Rica: (-18.5439°, -53.1292°)",
      "  Campos Belos: (-13.0367°, -46.7717°)",
      "  Januária: (-15.4795°, -44.3652°)",
      "  Carlópolis: (-23.4250°, -49.7208°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5418.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 959903.03 km²",
      "FINAL ANSWER: Area: 959903.03 km², Perimeter: 5418.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -11.45528,
        "lon": -41.43611,
        "name": "América Dourada"
      },
      {
        "lat": -19.75,
        "lon": -43.0375,
        "name": "Nova Era"
      },
      {
        "lat": -1.22361,
        "lon": -48.29444,
        "name": "Santa Bárbara do Pará"
      },
      {
        "lat": -4.22583,
        "lon": -38.73056,
        "name": "Redenção"
      },
      {
        "lat": -6.22944,
        "lon": -36.02278,
        "name": "Santa Cruz"
      },
      {
        "lat": -14.28361,
        "lon": -39.84278,
        "name": "Itagibá"
      }
    ],
    "ground_truth": {
      "area_km2": 1230137.85,
      "perimeter_km": 5909.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  América Dourada: (-11.4553°, -41.4361°)",
      "  Nova Era: (-19.7500°, -43.0375°)",
      "  Santa Bárbara do Pará: (-1.2236°, -48.2944°)",
      "  Redenção: (-4.2258°, -38.7306°)",
      "  Santa Cruz: (-6.2294°, -36.0228°)",
      "  Itagibá: (-14.2836°, -39.8428°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5909.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1230137.85 km²",
      "FINAL ANSWER: Area: 1230137.85 km², Perimeter: 5909.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.36718,
        "lon": 114.12347,
        "name": "Tai Wo Hau"
      },
      {
        "lat": 32.54278,
        "lon": 111.50861,
        "name": "Danjiangkou"
      },
      {
        "lat": 35.27814,
        "lon": 126.51181,
        "name": "Yeonggwang"
      },
      {
        "lat": 31.71667,
        "lon": 130.73333,
        "name": "Hamanoichi"
      }
    ],
    "ground_truth": {
      "area_km2": 1351571.91,
      "perimeter_km": 5075.34,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tai Wo Hau: (22.3672°, 114.1235°)",
      "  Danjiangkou: (32.5428°, 111.5086°)",
      "  Yeonggwang: (35.2781°, 126.5118°)",
      "  Hamanoichi: (31.7167°, 130.7333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5075.34 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1351571.91 km²",
      "FINAL ANSWER: Area: 1351571.91 km², Perimeter: 5075.34 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -8.07417,
        "lon": -39.11917,
        "name": "Salgueiro"
      },
      {
        "lat": -7.38917,
        "lon": -38.77444,
        "name": "Mauriti"
      },
      {
        "lat": -4.28694,
        "lon": -38.64306,
        "name": "Barreira"
      },
      {
        "lat": -7.59111,
        "lon": -35.49139,
        "name": "São Vicente Férrer"
      },
      {
        "lat": -10.7375,
        "lon": -37.08167,
        "name": "Maruim"
      }
    ],
    "ground_truth": {
      "area_km2": 153973.7,
      "perimeter_km": 1698.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Salgueiro: (-8.0742°, -39.1192°)",
      "  Mauriti: (-7.3892°, -38.7744°)",
      "  Barreira: (-4.2869°, -38.6431°)",
      "  São Vicente Férrer: (-7.5911°, -35.4914°)",
      "  Maruim: (-10.7375°, -37.0817°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1698.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 153973.70 km²",
      "FINAL ANSWER: Area: 153973.70 km², Perimeter: 1698.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 42.39282,
        "lon": -83.04964,
        "name": "Hamtramck"
      },
      {
        "lat": 45.5608,
        "lon": -94.16249,
        "name": "Saint Cloud"
      },
      {
        "lat": 42.33704,
        "lon": -71.20922,
        "name": "Newton"
      },
      {
        "lat": 39.49983,
        "lon": -76.64108,
        "name": "Hunt Valley"
      }
    ],
    "ground_truth": {
      "area_km2": 390459.1,
      "perimeter_km": 4002.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hamtramck: (42.3928°, -83.0496°)",
      "  Saint Cloud: (45.5608°, -94.1625°)",
      "  Newton: (42.3370°, -71.2092°)",
      "  Hunt Valley: (39.4998°, -76.6411°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4002.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 390459.10 km²",
      "FINAL ANSWER: Area: 390459.10 km², Perimeter: 4002.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -10.06806,
        "lon": -78.15222,
        "name": "Huarmey"
      },
      {
        "lat": -7.73291,
        "lon": -79.3015,
        "name": "Paiján"
      },
      {
        "lat": 0.34881,
        "lon": -78.12462,
        "name": "Ibarra"
      },
      {
        "lat": 5.25397,
        "lon": -75.15403,
        "name": "Manzanares"
      },
      {
        "lat": 5.06692,
        "lon": -74.59499,
        "name": "Guaduas"
      }
    ],
    "ground_truth": {
      "area_km2": 321715.71,
      "perimeter_km": 3627.94,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Huarmey: (-10.0681°, -78.1522°)",
      "  Paiján: (-7.7329°, -79.3015°)",
      "  Ibarra: (0.3488°, -78.1246°)",
      "  Manzanares: (5.2540°, -75.1540°)",
      "  Guaduas: (5.0669°, -74.5950°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3627.94 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 321715.71 km²",
      "FINAL ANSWER: Area: 321715.71 km², Perimeter: 3627.94 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -33.93462,
        "lon": 18.86676,
        "name": "Stellenbosch"
      },
      {
        "lat": -33.4608,
        "lon": 18.72714,
        "name": "Malmesbury"
      },
      {
        "lat": -26.26781,
        "lon": 27.85849,
        "name": "Soweto"
      },
      {
        "lat": -29.12107,
        "lon": 26.214,
        "name": "Bloemfontein"
      },
      {
        "lat": -29.19448,
        "lon": 27.45739,
        "name": "Ladybrand"
      }
    ],
    "ground_truth": {
      "area_km2": 127421.52,
      "perimeter_km": 2689.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Stellenbosch: (-33.9346°, 18.8668°)",
      "  Malmesbury: (-33.4608°, 18.7271°)",
      "  Soweto: (-26.2678°, 27.8585°)",
      "  Bloemfontein: (-29.1211°, 26.2140°)",
      "  Ladybrand: (-29.1945°, 27.4574°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2689.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 127421.52 km²",
      "FINAL ANSWER: Area: 127421.52 km², Perimeter: 2689.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 26.31841,
        "lon": -80.09977,
        "name": "Deerfield Beach"
      },
      {
        "lat": 40.12617,
        "lon": -82.92907,
        "name": "Westerville"
      },
      {
        "lat": 40.60177,
        "lon": -73.99403,
        "name": "Bensonhurst"
      },
      {
        "lat": 41.94454,
        "lon": -71.28561,
        "name": "Attleboro"
      }
    ],
    "ground_truth": {
      "area_km2": 722725.94,
      "perimeter_km": 4502.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Deerfield Beach: (26.3184°, -80.0998°)",
      "  Westerville: (40.1262°, -82.9291°)",
      "  Bensonhurst: (40.6018°, -73.9940°)",
      "  Attleboro: (41.9445°, -71.2856°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4502.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 722725.94 km²",
      "FINAL ANSWER: Area: 722725.94 km², Perimeter: 4502.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.8527,
        "lon": -7.03171,
        "name": "Skhirate"
      },
      {
        "lat": -36.61617,
        "lon": -64.28991,
        "name": "Santa Rosa"
      },
      {
        "lat": 36.09569,
        "lon": -79.4378,
        "name": "Burlington"
      },
      {
        "lat": -6.97038,
        "lon": 109.64794,
        "name": "Kedungwuni"
      },
      {
        "lat": 50.87309,
        "lon": 4.33419,
        "name": "Jette"
      }
    ],
    "ground_truth": {
      "area_km2": 105047634.88,
      "perimeter_km": 48441.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Skhirate: (33.8527°, -7.0317°)",
      "  Santa Rosa: (-36.6162°, -64.2899°)",
      "  Burlington: (36.0957°, -79.4378°)",
      "  Kedungwuni: (-6.9704°, 109.6479°)",
      "  Jette: (50.8731°, 4.3342°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 48441.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 105047634.88 km²",
      "FINAL ANSWER: Area: 105047634.88 km², Perimeter: 48441.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.29876,
        "lon": -90.18481,
        "name": "Jackson"
      },
      {
        "lat": 40.87589,
        "lon": -81.40234,
        "name": "North Canton"
      },
      {
        "lat": 43.85012,
        "lon": -79.03288,
        "name": "Ajax"
      },
      {
        "lat": 39.36415,
        "lon": -74.42306,
        "name": "Atlantic City"
      },
      {
        "lat": 35.26208,
        "lon": -81.1873,
        "name": "Gastonia"
      }
    ],
    "ground_truth": {
      "area_km2": 669499.74,
      "perimeter_km": 3891.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Jackson: (32.2988°, -90.1848°)",
      "  North Canton: (40.8759°, -81.4023°)",
      "  Ajax: (43.8501°, -79.0329°)",
      "  Atlantic City: (39.3642°, -74.4231°)",
      "  Gastonia: (35.2621°, -81.1873°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3891.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 669499.74 km²",
      "FINAL ANSWER: Area: 669499.74 km², Perimeter: 3891.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.72727,
        "lon": -89.21675,
        "name": "Carbondale"
      },
      {
        "lat": 45.3001,
        "lon": -75.91606,
        "name": "Kanata"
      },
      {
        "lat": 45.5152,
        "lon": -73.46818,
        "name": "Longueuil"
      },
      {
        "lat": 42.3501,
        "lon": -71.15644,
        "name": "Brighton"
      },
      {
        "lat": 40.8126,
        "lon": -73.88402,
        "name": "Hunts Point"
      },
      {
        "lat": 39.32928,
        "lon": -76.54463,
        "name": "Frankford"
      }
    ],
    "ground_truth": {
      "area_km2": 543716.69,
      "perimeter_km": 3658.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Carbondale: (37.7273°, -89.2168°)",
      "  Kanata: (45.3001°, -75.9161°)",
      "  Longueuil: (45.5152°, -73.4682°)",
      "  Brighton: (42.3501°, -71.1564°)",
      "  Hunts Point: (40.8126°, -73.8840°)",
      "  Frankford: (39.3293°, -76.5446°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3658.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 543716.69 km²",
      "FINAL ANSWER: Area: 543716.69 km², Perimeter: 3658.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.82289,
        "lon": 147.61041,
        "name": "Bairnsdale"
      },
      {
        "lat": -37.83382,
        "lon": 144.93834,
        "name": "City of Port Phillip"
      },
      {
        "lat": -38.14711,
        "lon": 144.36069,
        "name": "Geelong"
      },
      {
        "lat": -27.56056,
        "lon": 151.95386,
        "name": "Toowoomba"
      },
      {
        "lat": -33.52314,
        "lon": 151.31325,
        "name": "Umina Beach"
      },
      {
        "lat": -33.95,
        "lon": 151.13333,
        "name": "Rockdale"
      }
    ],
    "ground_truth": {
      "area_km2": 253381.39,
      "perimeter_km": 2920.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bairnsdale: (-37.8229°, 147.6104°)",
      "  City of Port Phillip: (-37.8338°, 144.9383°)",
      "  Geelong: (-38.1471°, 144.3607°)",
      "  Toowoomba: (-27.5606°, 151.9539°)",
      "  Umina Beach: (-33.5231°, 151.3133°)",
      "  Rockdale: (-33.9500°, 151.1333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2920.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 253381.39 km²",
      "FINAL ANSWER: Area: 253381.39 km², Perimeter: 2920.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -34.78254,
        "lon": 138.61077,
        "name": "Parafield Gardens"
      },
      {
        "lat": -19.26639,
        "lon": 146.80569,
        "name": "Townsville"
      },
      {
        "lat": -27.63917,
        "lon": 153.10944,
        "name": "Logan City"
      },
      {
        "lat": -33.79798,
        "lon": 151.28826,
        "name": "Manly"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 1322031.56,
      "perimeter_km": 4945.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Parafield Gardens: (-34.7825°, 138.6108°)",
      "  Townsville: (-19.2664°, 146.8057°)",
      "  Logan City: (-27.6392°, 153.1094°)",
      "  Manly: (-33.7980°, 151.2883°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4945.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1322031.56 km²",
      "FINAL ANSWER: Area: 1322031.56 km², Perimeter: 4945.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 1.3651,
        "lon": 104.1118,
        "name": "Pengerang"
      },
      {
        "lat": 2.2635,
        "lon": 102.2179,
        "name": "Kampung Cheng"
      },
      {
        "lat": 16.63557,
        "lon": 97.61526,
        "name": "Hmaw Bi"
      },
      {
        "lat": -0.49167,
        "lon": 117.14583,
        "name": "Samarinda"
      }
    ],
    "ground_truth": {
      "area_km2": 1330525.31,
      "perimeter_km": 6238.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pengerang: (1.3651°, 104.1118°)",
      "  Kampung Cheng: (2.2635°, 102.2179°)",
      "  Hmaw Bi: (16.6356°, 97.6153°)",
      "  Samarinda: (-0.4917°, 117.1458°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6238.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1330525.31 km²",
      "FINAL ANSWER: Area: 1330525.31 km², Perimeter: 6238.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 30.17173,
        "lon": 107.22991,
        "name": "Haitang"
      },
      {
        "lat": 34.73564,
        "lon": 105.32632,
        "name": "Gangu Chengguanzhen"
      },
      {
        "lat": 36.95389,
        "lon": 118.10472,
        "name": "Suozhen"
      },
      {
        "lat": 20.03421,
        "lon": 110.34651,
        "name": "Haikou"
      }
    ],
    "ground_truth": {
      "area_km2": 997750.09,
      "perimeter_km": 4911.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Haitang: (30.1717°, 107.2299°)",
      "  Gangu Chengguanzhen: (34.7356°, 105.3263°)",
      "  Suozhen: (36.9539°, 118.1047°)",
      "  Haikou: (20.0342°, 110.3465°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4911.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 997750.09 km²",
      "FINAL ANSWER: Area: 997750.09 km², Perimeter: 4911.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 5.20913,
        "lon": -1.06058,
        "name": "Saltpond"
      },
      {
        "lat": 7.92807,
        "lon": 1.97558,
        "name": "Savalou"
      },
      {
        "lat": 10.49222,
        "lon": 0.99972,
        "name": "Cobly"
      },
      {
        "lat": 5.1009,
        "lon": 6.81411,
        "name": "Elele"
      },
      {
        "lat": 6.41502,
        "lon": 2.88132,
        "name": "Badagry"
      }
    ],
    "ground_truth": {
      "area_km2": 382074.67,
      "perimeter_km": 2548.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Saltpond: (5.2091°, -1.0606°)",
      "  Savalou: (7.9281°, 1.9756°)",
      "  Cobly: (10.4922°, 0.9997°)",
      "  Elele: (5.1009°, 6.8141°)",
      "  Badagry: (6.4150°, 2.8813°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2548.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 382074.67 km²",
      "FINAL ANSWER: Area: 382074.67 km², Perimeter: 2548.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 47.17941,
        "lon": -1.62468,
        "name": "Bouguenais"
      },
      {
        "lat": 49.62612,
        "lon": -1.64349,
        "name": "Octeville"
      },
      {
        "lat": 51.43092,
        "lon": -0.50606,
        "name": "Staines"
      },
      {
        "lat": 48.75329,
        "lon": 2.29668,
        "name": "Antony"
      }
    ],
    "ground_truth": {
      "area_km2": 71818.86,
      "perimeter_km": 1187.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bouguenais: (47.1794°, -1.6247°)",
      "  Octeville: (49.6261°, -1.6435°)",
      "  Staines: (51.4309°, -0.5061°)",
      "  Antony: (48.7533°, 2.2967°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1187.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 71818.86 km²",
      "FINAL ANSWER: Area: 71818.86 km², Perimeter: 1187.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.01539,
        "lon": 23.69187,
        "name": "Peristéri"
      },
      {
        "lat": 45.59665,
        "lon": 9.88688,
        "name": "Palazzolo sull'Oglio"
      },
      {
        "lat": 52.67631,
        "lon": 13.27775,
        "name": "Hohen Neuendorf"
      },
      {
        "lat": 58.59382,
        "lon": 35.80244,
        "name": "Pestovo"
      },
      {
        "lat": 55.86667,
        "lon": 37.58333,
        "name": "Slobodka"
      },
      {
        "lat": 48.50834,
        "lon": 32.26618,
        "name": "Kropyvnytskyy"
      }
    ],
    "ground_truth": {
      "area_km2": 2406360.85,
      "perimeter_km": 6363.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Peristéri: (38.0154°, 23.6919°)",
      "  Palazzolo sull'Oglio: (45.5966°, 9.8869°)",
      "  Hohen Neuendorf: (52.6763°, 13.2777°)",
      "  Pestovo: (58.5938°, 35.8024°)",
      "  Slobodka: (55.8667°, 37.5833°)",
      "  Kropyvnytskyy: (48.5083°, 32.2662°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6363.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2406360.85 km²",
      "FINAL ANSWER: Area: 2406360.85 km², Perimeter: 6363.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 6.1162,
        "lon": -6.53603,
        "name": "Grand-Zattry"
      },
      {
        "lat": 14.00776,
        "lon": 0.75306,
        "name": "Téra"
      },
      {
        "lat": 5.71417,
        "lon": -0.15418,
        "name": "Adenta"
      }
    ],
    "ground_truth": {
      "area_km2": 328743.22,
      "perimeter_km": 2820.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Grand-Zattry: (6.1162°, -6.5360°)",
      "  Téra: (14.0078°, 0.7531°)",
      "  Adenta: (5.7142°, -0.1542°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2820.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 328743.22 km²",
      "FINAL ANSWER: Area: 328743.22 km², Perimeter: 2820.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.18972,
        "lon": -46.98028,
        "name": "Monte Santo de Minas"
      },
      {
        "lat": -17.31472,
        "lon": -53.21528,
        "name": "Alto Araguaia"
      },
      {
        "lat": -15.76194,
        "lon": -48.28167,
        "name": "Águas Lindas de Goiás"
      },
      {
        "lat": -6.24444,
        "lon": -38.91361,
        "name": "Orós"
      },
      {
        "lat": -11.13556,
        "lon": -42.11278,
        "name": "Central"
      },
      {
        "lat": -18.37333,
        "lon": -40.83056,
        "name": "Ecoporanga"
      }
    ],
    "ground_truth": {
      "area_km2": 900117.01,
      "perimeter_km": 4987.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Monte Santo de Minas: (-21.1897°, -46.9803°)",
      "  Alto Araguaia: (-17.3147°, -53.2153°)",
      "  Águas Lindas de Goiás: (-15.7619°, -48.2817°)",
      "  Orós: (-6.2444°, -38.9136°)",
      "  Central: (-11.1356°, -42.1128°)",
      "  Ecoporanga: (-18.3733°, -40.8306°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4987.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 900117.01 km²",
      "FINAL ANSWER: Area: 900117.01 km², Perimeter: 4987.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.06396,
        "lon": -80.72091,
        "name": "Wheeling"
      },
      {
        "lat": 39.43534,
        "lon": -84.20299,
        "name": "Lebanon"
      },
      {
        "lat": 43.73766,
        "lon": -79.34972,
        "name": "Banbury-Don Mills"
      },
      {
        "lat": 42.52509,
        "lon": -71.75979,
        "name": "Leominster"
      },
      {
        "lat": 36.71709,
        "lon": -76.59023,
        "name": "South Suffolk"
      }
    ],
    "ground_truth": {
      "area_km2": 381570.07,
      "perimeter_km": 2846.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Wheeling: (40.0640°, -80.7209°)",
      "  Lebanon: (39.4353°, -84.2030°)",
      "  Banbury-Don Mills: (43.7377°, -79.3497°)",
      "  Leominster: (42.5251°, -71.7598°)",
      "  South Suffolk: (36.7171°, -76.5902°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2846.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 381570.07 km²",
      "FINAL ANSWER: Area: 381570.07 km², Perimeter: 2846.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 36.13968,
        "lon": -120.36015,
        "name": "Coalinga"
      },
      {
        "lat": 35.14778,
        "lon": -114.5683,
        "name": "Bullhead City"
      },
      {
        "lat": 33.24866,
        "lon": -111.6343,
        "name": "Queen Creek"
      },
      {
        "lat": 34.23087,
        "lon": -111.32514,
        "name": "Payson"
      },
      {
        "lat": 20.23031,
        "lon": -99.21396,
        "name": "Mixquiahuala de Juarez"
      }
    ],
    "ground_truth": {
      "area_km2": 537972.1,
      "perimeter_km": 5664.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Coalinga: (36.1397°, -120.3602°)",
      "  Bullhead City: (35.1478°, -114.5683°)",
      "  Queen Creek: (33.2487°, -111.6343°)",
      "  Payson: (34.2309°, -111.3251°)",
      "  Mixquiahuala de Juarez: (20.2303°, -99.2140°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5664.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 537972.10 km²",
      "FINAL ANSWER: Area: 537972.10 km², Perimeter: 5664.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 31.28244,
        "lon": -4.26541,
        "name": "Moulay Ali Cherif"
      },
      {
        "lat": 35.23464,
        "lon": -0.24435,
        "name": "Sfizef"
      },
      {
        "lat": 36.66774,
        "lon": 3.59115,
        "name": "Beni Amrane"
      },
      {
        "lat": 36.33293,
        "lon": 5.08843,
        "name": "Bougaa"
      },
      {
        "lat": 27.05,
        "lon": 14.4,
        "name": "Al Jadīd"
      }
    ],
    "ground_truth": {
      "area_km2": 780380.15,
      "perimeter_km": 4321.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Moulay Ali Cherif: (31.2824°, -4.2654°)",
      "  Sfizef: (35.2346°, -0.2444°)",
      "  Beni Amrane: (36.6677°, 3.5911°)",
      "  Bougaa: (36.3329°, 5.0884°)",
      "  Al Jadīd: (27.0500°, 14.4000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4321.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 780380.15 km²",
      "FINAL ANSWER: Area: 780380.15 km², Perimeter: 4321.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 19.68006,
        "lon": -103.2514,
        "name": "Tamazula de Gordiano"
      },
      {
        "lat": 33.44179,
        "lon": -94.03769,
        "name": "Texarkana"
      },
      {
        "lat": 25.90175,
        "lon": -97.49748,
        "name": "Brownsville"
      }
    ],
    "ground_truth": {
      "area_km2": 146181.76,
      "perimeter_km": 3592.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tamazula de Gordiano: (19.6801°, -103.2514°)",
      "  Texarkana: (33.4418°, -94.0377°)",
      "  Brownsville: (25.9017°, -97.4975°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3592.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 146181.76 km²",
      "FINAL ANSWER: Area: 146181.76 km², Perimeter: 3592.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -35.73167,
        "lon": 174.32391,
        "name": "Whangarei"
      },
      {
        "lat": -36.93754,
        "lon": 174.65584,
        "name": "Titirangi"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      }
    ],
    "ground_truth": {
      "area_km2": 69280.78,
      "perimeter_km": 1463.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  Whangarei: (-35.7317°, 174.3239°)",
      "  Titirangi: (-36.9375°, 174.6558°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1463.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 69280.78 km²",
      "FINAL ANSWER: Area: 69280.78 km², Perimeter: 1463.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.27784,
        "lon": -123.12794,
        "name": "Downtown"
      },
      {
        "lat": 37.05828,
        "lon": -120.84992,
        "name": "Los Banos"
      },
      {
        "lat": 37.6391,
        "lon": -120.99688,
        "name": "Modesto"
      }
    ],
    "ground_truth": {
      "area_km2": 3439.7,
      "perimeter_km": 2742.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Downtown: (49.2778°, -123.1279°)",
      "  Los Banos: (37.0583°, -120.8499°)",
      "  Modesto: (37.6391°, -120.9969°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2742.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3439.70 km²",
      "FINAL ANSWER: Area: 3439.70 km², Perimeter: 2742.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 48.98333,
        "lon": 2.23333,
        "name": "Franconville"
      },
      {
        "lat": 53.47497,
        "lon": -2.08809,
        "name": "Dukinfield"
      },
      {
        "lat": 51.38333,
        "lon": 8.08333,
        "name": "Arnsberg"
      },
      {
        "lat": 50.32174,
        "lon": 10.20673,
        "name": "Bad Neustadt an der Saale"
      }
    ],
    "ground_truth": {
      "area_km2": 187181.51,
      "perimeter_km": 2092.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Franconville: (48.9833°, 2.2333°)",
      "  Dukinfield: (53.4750°, -2.0881°)",
      "  Arnsberg: (51.3833°, 8.0833°)",
      "  Bad Neustadt an der Saale: (50.3217°, 10.2067°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2092.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 187181.51 km²",
      "FINAL ANSWER: Area: 187181.51 km², Perimeter: 2092.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.58508,
        "lon": 5.00268,
        "name": "Miramas"
      },
      {
        "lat": 54.53478,
        "lon": -1.05606,
        "name": "Guisborough"
      },
      {
        "lat": 54.03374,
        "lon": 22.50704,
        "name": "Olecko"
      },
      {
        "lat": 49.86899,
        "lon": 8.9321,
        "name": "Groß-Umstadt"
      }
    ],
    "ground_truth": {
      "area_km2": 1177958.0,
      "perimeter_km": 4614.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Miramas: (43.5851°, 5.0027°)",
      "  Guisborough: (54.5348°, -1.0561°)",
      "  Olecko: (54.0337°, 22.5070°)",
      "  Groß-Umstadt: (49.8690°, 8.9321°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4614.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1177958.00 km²",
      "FINAL ANSWER: Area: 1177958.00 km², Perimeter: 4614.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.89969,
        "lon": -50.20821,
        "name": "Bagre"
      },
      {
        "lat": -22.4325,
        "lon": -46.5725,
        "name": "Monte Sião"
      },
      {
        "lat": -17.29972,
        "lon": -48.27944,
        "name": "Pires do Rio"
      }
    ],
    "ground_truth": {
      "area_km2": 89512.49,
      "perimeter_km": 4639.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Bagre: (-1.8997°, -50.2082°)",
      "  Monte Sião: (-22.4325°, -46.5725°)",
      "  Pires do Rio: (-17.2997°, -48.2794°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4639.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 89512.49 km²",
      "FINAL ANSWER: Area: 89512.49 km², Perimeter: 4639.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.9526,
        "lon": -84.54993,
        "name": "Marietta"
      },
      {
        "lat": 42.1103,
        "lon": -88.03424,
        "name": "Palatine"
      },
      {
        "lat": 44.88969,
        "lon": -93.34995,
        "name": "Edina"
      },
      {
        "lat": 41.39482,
        "lon": -73.45401,
        "name": "Danbury"
      },
      {
        "lat": 40.84288,
        "lon": -73.29289,
        "name": "Commack"
      }
    ],
    "ground_truth": {
      "area_km2": 1063190.04,
      "perimeter_km": 4457.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Marietta: (33.9526°, -84.5499°)",
      "  Palatine: (42.1103°, -88.0342°)",
      "  Edina: (44.8897°, -93.3500°)",
      "  Danbury: (41.3948°, -73.4540°)",
      "  Commack: (40.8429°, -73.2929°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4457.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1063190.04 km²",
      "FINAL ANSWER: Area: 1063190.04 km², Perimeter: 4457.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.88264,
        "lon": 144.7003,
        "name": "Hoppers Crossing"
      },
      {
        "lat": -36.35846,
        "lon": 146.32056,
        "name": "Wangaratta"
      },
      {
        "lat": -33.78333,
        "lon": 150.93333,
        "name": "Seven Hills"
      },
      {
        "lat": -35.41647,
        "lon": 149.06954,
        "name": "Tuggeranong Administrative District"
      }
    ],
    "ground_truth": {
      "area_km2": 26910.48,
      "perimeter_km": 1455.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Hoppers Crossing: (-37.8826°, 144.7003°)",
      "  Wangaratta: (-36.3585°, 146.3206°)",
      "  Seven Hills: (-33.7833°, 150.9333°)",
      "  Tuggeranong Administrative District: (-35.4165°, 149.0695°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1455.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 26910.48 km²",
      "FINAL ANSWER: Area: 26910.48 km², Perimeter: 1455.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -44.39672,
        "lon": 171.25364,
        "name": "Timaru"
      },
      {
        "lat": -36.8582,
        "lon": 174.62019,
        "name": "Lincoln"
      },
      {
        "lat": -37.78821,
        "lon": 175.2902,
        "name": "Hamilton East"
      }
    ],
    "ground_truth": {
      "area_km2": 38765.86,
      "perimeter_km": 1812.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Timaru: (-44.3967°, 171.2536°)",
      "  Lincoln: (-36.8582°, 174.6202°)",
      "  Hamilton East: (-37.7882°, 175.2902°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1812.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 38765.86 km²",
      "FINAL ANSWER: Area: 38765.86 km², Perimeter: 1812.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.75705,
        "lon": 138.60819,
        "name": "Paralowie"
      },
      {
        "lat": -33.28397,
        "lon": 149.10018,
        "name": "Orange"
      },
      {
        "lat": -37.81501,
        "lon": 144.96657,
        "name": "Melbourne City Centre"
      }
    ],
    "ground_truth": {
      "area_km2": 206000.92,
      "perimeter_km": 2270.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Paralowie: (-34.7570°, 138.6082°)",
      "  Orange: (-33.2840°, 149.1002°)",
      "  Melbourne City Centre: (-37.8150°, 144.9666°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2270.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 206000.92 km²",
      "FINAL ANSWER: Area: 206000.92 km², Perimeter: 2270.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.34381,
        "lon": 3.22475,
        "name": "’Aïn el Bell"
      },
      {
        "lat": 35.93115,
        "lon": 0.08918,
        "name": "Mostaganem"
      },
      {
        "lat": 36.67446,
        "lon": 10.15633,
        "name": "La Mohammedia"
      },
      {
        "lat": 35.82539,
        "lon": 10.63699,
        "name": "Sousse"
      }
    ],
    "ground_truth": {
      "area_km2": 130847.39,
      "perimeter_km": 2038.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  ’Aïn el Bell: (34.3438°, 3.2247°)",
      "  Mostaganem: (35.9312°, 0.0892°)",
      "  La Mohammedia: (36.6745°, 10.1563°)",
      "  Sousse: (35.8254°, 10.6370°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2038.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 130847.39 km²",
      "FINAL ANSWER: Area: 130847.39 km², Perimeter: 2038.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -42.76848,
        "lon": -65.03827,
        "name": "Puerto Madryn"
      },
      {
        "lat": -32.83369,
        "lon": -70.59827,
        "name": "Los Andes"
      },
      {
        "lat": -32.17675,
        "lon": -64.11295,
        "name": "Río Tercero"
      },
      {
        "lat": -27.80047,
        "lon": -64.26285,
        "name": "Santiago del Estero"
      },
      {
        "lat": -29.37639,
        "lon": -51.11444,
        "name": "Nova Petrópolis"
      },
      {
        "lat": -29.91778,
        "lon": -51.18361,
        "name": "Canoas"
      }
    ],
    "ground_truth": {
      "area_km2": 1484740.75,
      "perimeter_km": 5549.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Puerto Madryn: (-42.7685°, -65.0383°)",
      "  Los Andes: (-32.8337°, -70.5983°)",
      "  Río Tercero: (-32.1767°, -64.1129°)",
      "  Santiago del Estero: (-27.8005°, -64.2629°)",
      "  Nova Petrópolis: (-29.3764°, -51.1144°)",
      "  Canoas: (-29.9178°, -51.1836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5549.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1484740.75 km²",
      "FINAL ANSWER: Area: 1484740.75 km², Perimeter: 5549.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.89013,
        "lon": 23.74406,
        "name": "Ellinikó"
      },
      {
        "lat": 59.51839,
        "lon": 17.91128,
        "name": "Upplands Väsby"
      },
      {
        "lat": 63.11418,
        "lon": 21.68216,
        "name": "Korsholm"
      },
      {
        "lat": 52.04479,
        "lon": 39.72569,
        "name": "Usman’"
      },
      {
        "lat": 48.2824,
        "lon": 37.17772,
        "name": "Pokrovsk"
      },
      {
        "lat": 44.0834,
        "lon": 41.9763,
        "name": "Ust’-Dzheguta"
      }
    ],
    "ground_truth": {
      "area_km2": 2592535.81,
      "perimeter_km": 7235.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Ellinikó: (37.8901°, 23.7441°)",
      "  Upplands Väsby: (59.5184°, 17.9113°)",
      "  Korsholm: (63.1142°, 21.6822°)",
      "  Usman’: (52.0448°, 39.7257°)",
      "  Pokrovsk: (48.2824°, 37.1777°)",
      "  Ust’-Dzheguta: (44.0834°, 41.9763°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7235.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2592535.81 km²",
      "FINAL ANSWER: Area: 2592535.81 km², Perimeter: 7235.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -30.72644,
        "lon": -64.80387,
        "name": "Cruz del Eje"
      },
      {
        "lat": -18.54389,
        "lon": -53.12917,
        "name": "Costa Rica"
      },
      {
        "lat": -20.08667,
        "lon": -51.09361,
        "name": "Aparecida do Taboado"
      },
      {
        "lat": -21.22583,
        "lon": -43.77361,
        "name": "Barbacena"
      },
      {
        "lat": -23.55242,
        "lon": -46.65735,
        "name": "Consolação"
      }
    ],
    "ground_truth": {
      "area_km2": 907518.54,
      "perimeter_km": 5194.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Cruz del Eje: (-30.7264°, -64.8039°)",
      "  Costa Rica: (-18.5439°, -53.1292°)",
      "  Aparecida do Taboado: (-20.0867°, -51.0936°)",
      "  Barbacena: (-21.2258°, -43.7736°)",
      "  Consolação: (-23.5524°, -46.6574°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5194.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 907518.54 km²",
      "FINAL ANSWER: Area: 907518.54 km², Perimeter: 5194.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -13.686,
        "lon": -39.47803,
        "name": "Wenceslau Guimarães"
      },
      {
        "lat": -9.91722,
        "lon": -37.27833,
        "name": "Porto da Folha"
      },
      {
        "lat": -7.50528,
        "lon": -35.31833,
        "name": "Timbaúba"
      }
    ],
    "ground_truth": {
      "area_km2": 13586.04,
      "perimeter_km": 1650.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wenceslau Guimarães: (-13.6860°, -39.4780°)",
      "  Porto da Folha: (-9.9172°, -37.2783°)",
      "  Timbaúba: (-7.5053°, -35.3183°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1650.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13586.04 km²",
      "FINAL ANSWER: Area: 13586.04 km², Perimeter: 1650.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 47.49702,
        "lon": 7.59172,
        "name": "Reinach"
      },
      {
        "lat": 51.86568,
        "lon": -2.2431,
        "name": "Gloucester"
      },
      {
        "lat": 53.4273,
        "lon": 14.51303,
        "name": "Świerczewo"
      },
      {
        "lat": 45.88333,
        "lon": 22.9,
        "name": "Deva"
      },
      {
        "lat": 40.57762,
        "lon": 17.03812,
        "name": "Palagiano"
      }
    ],
    "ground_truth": {
      "area_km2": 1167177.45,
      "perimeter_km": 4863.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Reinach: (47.4970°, 7.5917°)",
      "  Gloucester: (51.8657°, -2.2431°)",
      "  Świerczewo: (53.4273°, 14.5130°)",
      "  Deva: (45.8833°, 22.9000°)",
      "  Palagiano: (40.5776°, 17.0381°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4863.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1167177.45 km²",
      "FINAL ANSWER: Area: 1167177.45 km², Perimeter: 4863.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -23.5275,
        "lon": -46.9025,
        "name": "Jandira"
      },
      {
        "lat": -26.07361,
        "lon": -53.72528,
        "name": "Santo Antônio do Sudoeste"
      },
      {
        "lat": -14.06944,
        "lon": -42.475,
        "name": "Caetité"
      },
      {
        "lat": -8.07361,
        "lon": -37.26444,
        "name": "Sertânia"
      },
      {
        "lat": -20.12389,
        "lon": -42.00139,
        "name": "Simonésia"
      },
      {
        "lat": -19.81,
        "lon": -43.17361,
        "name": "João Monlevade"
      }
    ],
    "ground_truth": {
      "area_km2": 708336.64,
      "perimeter_km": 5522.69,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Jandira: (-23.5275°, -46.9025°)",
      "  Santo Antônio do Sudoeste: (-26.0736°, -53.7253°)",
      "  Caetité: (-14.0694°, -42.4750°)",
      "  Sertânia: (-8.0736°, -37.2644°)",
      "  Simonésia: (-20.1239°, -42.0014°)",
      "  João Monlevade: (-19.8100°, -43.1736°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5522.69 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 708336.64 km²",
      "FINAL ANSWER: Area: 708336.64 km², Perimeter: 5522.69 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -2.63199,
        "lon": -80.38808,
        "name": "Playas"
      },
      {
        "lat": 5.69188,
        "lon": -76.65835,
        "name": "Quibdó"
      },
      {
        "lat": 5.13278,
        "lon": -74.15977,
        "name": "Pacho"
      },
      {
        "lat": 7.81348,
        "lon": -71.17788,
        "name": "Santa Bárbara"
      },
      {
        "lat": -12.08628,
        "lon": -75.20827,
        "name": "Chilca"
      }
    ],
    "ground_truth": {
      "area_km2": 1056058.41,
      "perimeter_km": 5195.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Playas: (-2.6320°, -80.3881°)",
      "  Quibdó: (5.6919°, -76.6583°)",
      "  Pacho: (5.1328°, -74.1598°)",
      "  Santa Bárbara: (7.8135°, -71.1779°)",
      "  Chilca: (-12.0863°, -75.2083°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5195.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1056058.41 km²",
      "FINAL ANSWER: Area: 1056058.41 km², Perimeter: 5195.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -23.59468,
        "lon": -46.54359,
        "name": "Sao Lucas"
      },
      {
        "lat": -22.7775,
        "lon": -47.29583,
        "name": "Nova Odessa"
      },
      {
        "lat": -6.60167,
        "lon": -44.07667,
        "name": "Pastos Bons"
      },
      {
        "lat": -11.00861,
        "lon": -44.51944,
        "name": "Santa Rita de Cássia"
      }
    ],
    "ground_truth": {
      "area_km2": 102705.46,
      "perimeter_km": 3858.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sao Lucas: (-23.5947°, -46.5436°)",
      "  Nova Odessa: (-22.7775°, -47.2958°)",
      "  Pastos Bons: (-6.6017°, -44.0767°)",
      "  Santa Rita de Cássia: (-11.0086°, -44.5194°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3858.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 102705.46 km²",
      "FINAL ANSWER: Area: 102705.46 km², Perimeter: 3858.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.85059,
        "lon": -87.79367,
        "name": "Berwyn"
      },
      {
        "lat": 43.76489,
        "lon": -79.52198,
        "name": "Black Creek"
      },
      {
        "lat": 44.77599,
        "lon": -63.67865,
        "name": "Lower Sackville"
      },
      {
        "lat": 40.73232,
        "lon": -74.23487,
        "name": "Irvington"
      }
    ],
    "ground_truth": {
      "area_km2": 403878.76,
      "perimeter_km": 4081.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Berwyn: (41.8506°, -87.7937°)",
      "  Black Creek: (43.7649°, -79.5220°)",
      "  Lower Sackville: (44.7760°, -63.6786°)",
      "  Irvington: (40.7323°, -74.2349°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4081.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 403878.76 km²",
      "FINAL ANSWER: Area: 403878.76 km², Perimeter: 4081.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -41.05584,
        "lon": 145.90375,
        "name": "Burnie"
      },
      {
        "lat": -37.87397,
        "lon": 145.04253,
        "name": "Malvern East"
      },
      {
        "lat": -20.72523,
        "lon": 139.49727,
        "name": "Mount Isa"
      },
      {
        "lat": -27.19354,
        "lon": 153.02631,
        "name": "Deception Bay"
      },
      {
        "lat": -30.29626,
        "lon": 153.11351,
        "name": "Coffs Harbour"
      },
      {
        "lat": -33.78269,
        "lon": 151.04888,
        "name": "Carlingford"
      }
    ],
    "ground_truth": {
      "area_km2": 1458150.81,
      "perimeter_km": 5597.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Burnie: (-41.0558°, 145.9038°)",
      "  Malvern East: (-37.8740°, 145.0425°)",
      "  Mount Isa: (-20.7252°, 139.4973°)",
      "  Deception Bay: (-27.1935°, 153.0263°)",
      "  Coffs Harbour: (-30.2963°, 153.1135°)",
      "  Carlingford: (-33.7827°, 151.0489°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5597.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1458150.81 km²",
      "FINAL ANSWER: Area: 1458150.81 km², Perimeter: 5597.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.05154,
        "lon": -75.26775,
        "name": "San Pablo"
      },
      {
        "lat": 10.96854,
        "lon": -74.78132,
        "name": "Barranquilla"
      },
      {
        "lat": 8.39925,
        "lon": -71.64082,
        "name": "Santa Cruz de Mora"
      },
      {
        "lat": -7.05056,
        "lon": -71.69472,
        "name": "Ipixuna"
      }
    ],
    "ground_truth": {
      "area_km2": 369782.57,
      "perimeter_km": 4222.67,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  San Pablo: (10.0515°, -75.2678°)",
      "  Barranquilla: (10.9685°, -74.7813°)",
      "  Santa Cruz de Mora: (8.3993°, -71.6408°)",
      "  Ipixuna: (-7.0506°, -71.6947°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4222.67 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 369782.57 km²",
      "FINAL ANSWER: Area: 369782.57 km², Perimeter: 4222.67 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.66772,
        "lon": -111.93883,
        "name": "Taylorsville"
      },
      {
        "lat": 38.20007,
        "lon": -85.82274,
        "name": "Shively"
      },
      {
        "lat": 33.16262,
        "lon": -96.93751,
        "name": "Little Elm"
      }
    ],
    "ground_truth": {
      "area_km2": 850009.27,
      "perimeter_km": 4969.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Taylorsville: (40.6677°, -111.9388°)",
      "  Shively: (38.2001°, -85.8227°)",
      "  Little Elm: (33.1626°, -96.9375°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4969.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 850009.27 km²",
      "FINAL ANSWER: Area: 850009.27 km², Perimeter: 4969.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -7.3,
        "lon": 20.73333,
        "name": "Chitato"
      },
      {
        "lat": -3.28333,
        "lon": 31.52583,
        "name": "Uyovu"
      },
      {
        "lat": -3.49194,
        "lon": 31.96389,
        "name": "Ushirombo"
      },
      {
        "lat": -6.08125,
        "lon": 36.64657,
        "name": "Kibaigwa"
      }
    ],
    "ground_truth": {
      "area_km2": 318889.73,
      "perimeter_km": 3685.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Chitato: (-7.3000°, 20.7333°)",
      "  Uyovu: (-3.2833°, 31.5258°)",
      "  Ushirombo: (-3.4919°, 31.9639°)",
      "  Kibaigwa: (-6.0812°, 36.6466°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3685.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 318889.73 km²",
      "FINAL ANSWER: Area: 318889.73 km², Perimeter: 3685.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 13.95114,
        "lon": 101.71769,
        "name": "Kabin Buri"
      },
      {
        "lat": 29.32431,
        "lon": 107.76056,
        "name": "Wulong"
      },
      {
        "lat": 39.1375,
        "lon": 116.99972,
        "name": "Yangliuqing"
      },
      {
        "lat": 39.76538,
        "lon": 118.41191,
        "name": "Zhaogezhuang"
      },
      {
        "lat": 13.902,
        "lon": 121.0521,
        "name": "Cuenca"
      },
      {
        "lat": 22.28399,
        "lon": 114.14958,
        "name": "Mid Levels"
      }
    ],
    "ground_truth": {
      "area_km2": 4424513.23,
      "perimeter_km": 9016.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kabin Buri: (13.9511°, 101.7177°)",
      "  Wulong: (29.3243°, 107.7606°)",
      "  Yangliuqing: (39.1375°, 116.9997°)",
      "  Zhaogezhuang: (39.7654°, 118.4119°)",
      "  Cuenca: (13.9020°, 121.0521°)",
      "  Mid Levels: (22.2840°, 114.1496°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9016.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 4424513.23 km²",
      "FINAL ANSWER: Area: 4424513.23 km², Perimeter: 9016.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.09053,
        "lon": -6.34438,
        "name": "Lobakuya"
      },
      {
        "lat": 5.61411,
        "lon": -1.5502,
        "name": "Twifu Praso"
      },
      {
        "lat": 6.42611,
        "lon": 1.21333,
        "name": "Tsévié"
      },
      {
        "lat": 3.51667,
        "lon": 11.5,
        "name": "Mbalmayo"
      },
      {
        "lat": 0.00694,
        "lon": 15.63333,
        "name": "Makoua"
      },
      {
        "lat": -7.35207,
        "lon": 14.84629,
        "name": "Songo"
      }
    ],
    "ground_truth": {
      "area_km2": 1614370.22,
      "perimeter_km": 6190.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lobakuya: (5.0905°, -6.3444°)",
      "  Twifu Praso: (5.6141°, -1.5502°)",
      "  Tsévié: (6.4261°, 1.2133°)",
      "  Mbalmayo: (3.5167°, 11.5000°)",
      "  Makoua: (0.0069°, 15.6333°)",
      "  Songo: (-7.3521°, 14.8463°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6190.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1614370.22 km²",
      "FINAL ANSWER: Area: 1614370.22 km², Perimeter: 6190.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 29.14816,
        "lon": 31.12733,
        "name": "Būsh"
      },
      {
        "lat": 31.16844,
        "lon": 31.7655,
        "name": "Kafr al Kurdī"
      },
      {
        "lat": 30.31263,
        "lon": 32.30935,
        "name": "Fāyīd"
      },
      {
        "lat": 14.0012,
        "lon": 32.3116,
        "name": "Ad Douiem"
      }
    ],
    "ground_truth": {
      "area_km2": 113490.19,
      "perimeter_km": 3843.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Būsh: (29.1482°, 31.1273°)",
      "  Kafr al Kurdī: (31.1684°, 31.7655°)",
      "  Fāyīd: (30.3126°, 32.3094°)",
      "  Ad Douiem: (14.0012°, 32.3116°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3843.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 113490.19 km²",
      "FINAL ANSWER: Area: 113490.19 km², Perimeter: 3843.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -25.76972,
        "lon": -49.71583,
        "name": "Lapa"
      },
      {
        "lat": -23.56439,
        "lon": -46.61695,
        "name": "Cambuci"
      },
      {
        "lat": -20.31944,
        "lon": -40.33778,
        "name": "Vitória"
      }
    ],
    "ground_truth": {
      "area_km2": 27661.84,
      "perimeter_km": 2273.24,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lapa: (-25.7697°, -49.7158°)",
      "  Cambuci: (-23.5644°, -46.6170°)",
      "  Vitória: (-20.3194°, -40.3378°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2273.24 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 27661.84 km²",
      "FINAL ANSWER: Area: 27661.84 km², Perimeter: 2273.24 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.60075,
        "lon": 145.09555,
        "name": "Mernda"
      },
      {
        "lat": -27.98941,
        "lon": 153.33633,
        "name": "Nerang"
      },
      {
        "lat": -30.29626,
        "lon": 153.11351,
        "name": "Coffs Harbour"
      },
      {
        "lat": -33.92598,
        "lon": 151.19347,
        "name": "Mascot"
      }
    ],
    "ground_truth": {
      "area_km2": 150859.2,
      "perimeter_km": 2700.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mernda: (-37.6007°, 145.0956°)",
      "  Nerang: (-27.9894°, 153.3363°)",
      "  Coffs Harbour: (-30.2963°, 153.1135°)",
      "  Mascot: (-33.9260°, 151.1935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2700.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 150859.20 km²",
      "FINAL ANSWER: Area: 150859.20 km², Perimeter: 2700.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -31.83291,
        "lon": 115.7759,
        "name": "Duncraig"
      },
      {
        "lat": -32.32889,
        "lon": 115.83047,
        "name": "Baldivis"
      }
    ],
    "ground_truth": {
      "area_km2": 1617.7,
      "perimeter_km": 415.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Duncraig: (-31.8329°, 115.7759°)",
      "  Baldivis: (-32.3289°, 115.8305°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 415.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1617.70 km²",
      "FINAL ANSWER: Area: 1617.70 km², Perimeter: 415.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.4246,
        "lon": -3.68582,
        "name": "Recoletos"
      },
      {
        "lat": 53.70324,
        "lon": -0.87732,
        "name": "Goole"
      },
      {
        "lat": 50.01436,
        "lon": 8.35218,
        "name": "Hochheim am Main"
      }
    ],
    "ground_truth": {
      "area_km2": 530338.28,
      "perimeter_km": 3665.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Recoletos: (40.4246°, -3.6858°)",
      "  Goole: (53.7032°, -0.8773°)",
      "  Hochheim am Main: (50.0144°, 8.3522°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3665.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 530338.28 km²",
      "FINAL ANSWER: Area: 530338.28 km², Perimeter: 3665.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -19.73639,
        "lon": -45.25222,
        "name": "Bom Despacho"
      },
      {
        "lat": -5.52639,
        "lon": -47.49167,
        "name": "Imperatriz"
      },
      {
        "lat": -3.74194,
        "lon": -47.49472,
        "name": "Ulianópolis"
      },
      {
        "lat": -3.10056,
        "lon": -45.03361,
        "name": "Matinha"
      },
      {
        "lat": -3.68444,
        "lon": -42.75028,
        "name": "Brejo"
      },
      {
        "lat": -14.78556,
        "lon": -39.28028,
        "name": "Itabuna"
      }
    ],
    "ground_truth": {
      "area_km2": 1011098.48,
      "perimeter_km": 4472.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bom Despacho: (-19.7364°, -45.2522°)",
      "  Imperatriz: (-5.5264°, -47.4917°)",
      "  Ulianópolis: (-3.7419°, -47.4947°)",
      "  Matinha: (-3.1006°, -45.0336°)",
      "  Brejo: (-3.6844°, -42.7503°)",
      "  Itabuna: (-14.7856°, -39.2803°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4472.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1011098.48 km²",
      "FINAL ANSWER: Area: 1011098.48 km², Perimeter: 4472.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -32.5269,
        "lon": 115.7217,
        "name": "Mandurah"
      },
      {
        "lat": -31.89578,
        "lon": 115.76431,
        "name": "Scarborough"
      },
      {
        "lat": -28.77897,
        "lon": 114.61459,
        "name": "Geraldton"
      },
      {
        "lat": -23.69748,
        "lon": 133.88362,
        "name": "Alice Springs"
      }
    ],
    "ground_truth": {
      "area_km2": 781108.49,
      "perimeter_km": 4789.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Albany: (-35.0269°, 117.8837°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Mandurah: (-32.5269°, 115.7217°)",
      "  Scarborough: (-31.8958°, 115.7643°)",
      "  Geraldton: (-28.7790°, 114.6146°)",
      "  Alice Springs: (-23.6975°, 133.8836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4789.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 781108.49 km²",
      "FINAL ANSWER: Area: 781108.49 km², Perimeter: 4789.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 35.06544,
        "lon": 1.04945,
        "name": "Frenda"
      },
      {
        "lat": 36.75234,
        "lon": 4.3155,
        "name": "Freha"
      },
      {
        "lat": 36.50361,
        "lon": 7.44278,
        "name": "Héliopolis"
      }
    ],
    "ground_truth": {
      "area_km2": 28970.85,
      "perimeter_km": 1227.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Frenda: (35.0654°, 1.0494°)",
      "  Freha: (36.7523°, 4.3155°)",
      "  Héliopolis: (36.5036°, 7.4428°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1227.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 28970.85 km²",
      "FINAL ANSWER: Area: 28970.85 km², Perimeter: 1227.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 21.25993,
        "lon": -98.78935,
        "name": "Tamazunchale"
      },
      {
        "lat": 30.72353,
        "lon": -95.55078,
        "name": "Huntsville"
      },
      {
        "lat": 30.43826,
        "lon": -84.28073,
        "name": "Tallahassee"
      },
      {
        "lat": 22.41479,
        "lon": -80.2931,
        "name": "Lajas"
      },
      {
        "lat": 18.87309,
        "lon": -71.51656,
        "name": "Las Matas de Farfán"
      }
    ],
    "ground_truth": {
      "area_km2": 1795184.93,
      "perimeter_km": 7007.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tamazunchale: (21.2599°, -98.7893°)",
      "  Huntsville: (30.7235°, -95.5508°)",
      "  Tallahassee: (30.4383°, -84.2807°)",
      "  Lajas: (22.4148°, -80.2931°)",
      "  Las Matas de Farfán: (18.8731°, -71.5166°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7007.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1795184.93 km²",
      "FINAL ANSWER: Area: 1795184.93 km², Perimeter: 7007.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -25.47694,
        "lon": -48.83444,
        "name": "Morretes"
      },
      {
        "lat": -4.25528,
        "lon": -43.94056,
        "name": "Timbiras"
      },
      {
        "lat": -22.15847,
        "lon": -43.29321,
        "name": "Paraíba do Sul"
      }
    ],
    "ground_truth": {
      "area_km2": 575404.54,
      "perimeter_km": 5082.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Morretes: (-25.4769°, -48.8344°)",
      "  Timbiras: (-4.2553°, -43.9406°)",
      "  Paraíba do Sul: (-22.1585°, -43.2932°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5082.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 575404.54 km²",
      "FINAL ANSWER: Area: 575404.54 km², Perimeter: 5082.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -7.1955,
        "lon": 107.4313,
        "name": "Banjar"
      },
      {
        "lat": 14.51691,
        "lon": 121.2658,
        "name": "Baras"
      },
      {
        "lat": 13.2593,
        "lon": 123.4963,
        "name": "Oas"
      },
      {
        "lat": 9.6531,
        "lon": 124.3697,
        "name": "Jagna"
      },
      {
        "lat": 8.82778,
        "lon": 125.09972,
        "name": "Gingoog"
      },
      {
        "lat": -0.9516,
        "lon": 122.7875,
        "name": "Luwuk"
      }
    ],
    "ground_truth": {
      "area_km2": 1891259.35,
      "perimeter_km": 6624.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Banjar: (-7.1955°, 107.4313°)",
      "  Baras: (14.5169°, 121.2658°)",
      "  Oas: (13.2593°, 123.4963°)",
      "  Jagna: (9.6531°, 124.3697°)",
      "  Gingoog: (8.8278°, 125.0997°)",
      "  Luwuk: (-0.9516°, 122.7875°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6624.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1891259.35 km²",
      "FINAL ANSWER: Area: 1891259.35 km², Perimeter: 6624.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.74124,
        "lon": 144.73631,
        "name": "Caroline Springs"
      },
      {
        "lat": -36.75818,
        "lon": 144.28024,
        "name": "Bendigo"
      },
      {
        "lat": -33.91667,
        "lon": 151.03333,
        "name": "Bankstown"
      }
    ],
    "ground_truth": {
      "area_km2": 40022.13,
      "perimeter_km": 1514.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Caroline Springs: (-37.7412°, 144.7363°)",
      "  Bendigo: (-36.7582°, 144.2802°)",
      "  Bankstown: (-33.9167°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1514.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 40022.13 km²",
      "FINAL ANSWER: Area: 40022.13 km², Perimeter: 1514.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 12.70581,
        "lon": -7.90268,
        "name": "Sangarébougou"
      },
      {
        "lat": 13.25833,
        "lon": -0.21306,
        "name": "Mani"
      },
      {
        "lat": 9.04439,
        "lon": 6.57089,
        "name": "Lapai"
      },
      {
        "lat": 6.32485,
        "lon": 8.11368,
        "name": "Abakaliki"
      }
    ],
    "ground_truth": {
      "area_km2": 412283.95,
      "perimeter_km": 3951.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sangarébougou: (12.7058°, -7.9027°)",
      "  Mani: (13.2583°, -0.2131°)",
      "  Lapai: (9.0444°, 6.5709°)",
      "  Abakaliki: (6.3248°, 8.1137°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3951.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 412283.95 km²",
      "FINAL ANSWER: Area: 412283.95 km², Perimeter: 3951.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 17.21976,
        "lon": -100.63032,
        "name": "Técpan de Galeana"
      },
      {
        "lat": 19.88733,
        "lon": -102.20636,
        "name": "Tangancícuaro de Arista"
      },
      {
        "lat": 20.4925,
        "lon": -103.4175,
        "name": "Lomas del Sur"
      },
      {
        "lat": 19.90481,
        "lon": -99.34379,
        "name": "Tepeji del Río de Ocampo"
      },
      {
        "lat": 19.09917,
        "lon": -98.25417,
        "name": "Sanctorum"
      },
      {
        "lat": 18.94918,
        "lon": -97.80379,
        "name": "Los Reyes de Juárez"
      }
    ],
    "ground_truth": {
      "area_km2": 111248.08,
      "perimeter_km": 1463.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Técpan de Galeana: (17.2198°, -100.6303°)",
      "  Tangancícuaro de Arista: (19.8873°, -102.2064°)",
      "  Lomas del Sur: (20.4925°, -103.4175°)",
      "  Tepeji del Río de Ocampo: (19.9048°, -99.3438°)",
      "  Sanctorum: (19.0992°, -98.2542°)",
      "  Los Reyes de Juárez: (18.9492°, -97.8038°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1463.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 111248.08 km²",
      "FINAL ANSWER: Area: 111248.08 km², Perimeter: 1463.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.67307,
        "lon": -8.18087,
        "name": "Aoulouz"
      },
      {
        "lat": 35.07465,
        "lon": -1.22431,
        "name": "Bensekrane"
      },
      {
        "lat": 36.73829,
        "lon": 3.28079,
        "name": "Rouiba"
      }
    ],
    "ground_truth": {
      "area_km2": 29227.37,
      "perimeter_km": 2514.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Aoulouz: (30.6731°, -8.1809°)",
      "  Bensekrane: (35.0746°, -1.2243°)",
      "  Rouiba: (36.7383°, 3.2808°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2514.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 29227.37 km²",
      "FINAL ANSWER: Area: 29227.37 km², Perimeter: 2514.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 9.67826,
        "lon": 77.24951,
        "name": "Gudalur"
      },
      {
        "lat": 20.19718,
        "lon": 72.75035,
        "name": "Umargām"
      },
      {
        "lat": 19.79825,
        "lon": 85.82494,
        "name": "Puri"
      }
    ],
    "ground_truth": {
      "area_km2": 800040.33,
      "perimeter_km": 4085.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Gudalur: (9.6783°, 77.2495°)",
      "  Umargām: (20.1972°, 72.7503°)",
      "  Puri: (19.7982°, 85.8249°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4085.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 800040.33 km²",
      "FINAL ANSWER: Area: 800040.33 km², Perimeter: 4085.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 44.91608,
        "lon": -93.10161,
        "name": "West Saint Paul"
      },
      {
        "lat": 40.70788,
        "lon": -73.7868,
        "name": "Hillside"
      },
      {
        "lat": 39.46976,
        "lon": -76.8319,
        "name": "Reisterstown"
      }
    ],
    "ground_truth": {
      "area_km2": 184828.39,
      "perimeter_km": 3399.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  West Saint Paul: (44.9161°, -93.1016°)",
      "  Hillside: (40.7079°, -73.7868°)",
      "  Reisterstown: (39.4698°, -76.8319°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3399.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 184828.39 km²",
      "FINAL ANSWER: Area: 184828.39 km², Perimeter: 3399.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.19528,
        "lon": 146.5415,
        "name": "Traralgon"
      },
      {
        "lat": -37.91806,
        "lon": 145.03544,
        "name": "Bentleigh"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -33.76667,
        "lon": 150.81667,
        "name": "Mount Druitt"
      }
    ],
    "ground_truth": {
      "area_km2": 110690.45,
      "perimeter_km": 2156.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Traralgon: (-38.1953°, 146.5415°)",
      "  Bentleigh: (-37.9181°, 145.0354°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Mount Druitt: (-33.7667°, 150.8167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2156.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 110690.45 km²",
      "FINAL ANSWER: Area: 110690.45 km², Perimeter: 2156.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.79269,
        "lon": -9.1838,
        "name": "Odivelas"
      },
      {
        "lat": 52.07417,
        "lon": 4.35972,
        "name": "Voorburg"
      },
      {
        "lat": 51.01122,
        "lon": 13.82029,
        "name": "Leuben"
      }
    ],
    "ground_truth": {
      "area_km2": 503481.59,
      "perimeter_km": 4722.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Odivelas: (38.7927°, -9.1838°)",
      "  Voorburg: (52.0742°, 4.3597°)",
      "  Leuben: (51.0112°, 13.8203°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4722.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 503481.59 km²",
      "FINAL ANSWER: Area: 503481.59 km², Perimeter: 4722.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.5806,
        "lon": -112.23738,
        "name": "Peoria"
      },
      {
        "lat": 45.68456,
        "lon": -122.5751,
        "name": "Five Corners"
      },
      {
        "lat": 22.18912,
        "lon": -100.93792,
        "name": "Soledad de Graciano Sánchez"
      },
      {
        "lat": 32.43674,
        "lon": -111.22538,
        "name": "Marana"
      }
    ],
    "ground_truth": {
      "area_km2": 350925.57,
      "perimeter_km": 6556.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Peoria: (33.5806°, -112.2374°)",
      "  Five Corners: (45.6846°, -122.5751°)",
      "  Soledad de Graciano Sánchez: (22.1891°, -100.9379°)",
      "  Marana: (32.4367°, -111.2254°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6556.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 350925.57 km²",
      "FINAL ANSWER: Area: 350925.57 km², Perimeter: 6556.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -33.65249,
        "lon": 115.3455,
        "name": "Busselton"
      },
      {
        "lat": -32.27682,
        "lon": 115.72978,
        "name": "Rockingham"
      },
      {
        "lat": -28.77897,
        "lon": 114.61459,
        "name": "Geraldton"
      },
      {
        "lat": -31.8075,
        "lon": 115.86599,
        "name": "Landsdale"
      },
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      }
    ],
    "ground_truth": {
      "area_km2": 38124.51,
      "perimeter_km": 1654.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Busselton: (-33.6525°, 115.3455°)",
      "  Rockingham: (-32.2768°, 115.7298°)",
      "  Geraldton: (-28.7790°, 114.6146°)",
      "  Landsdale: (-31.8075°, 115.8660°)",
      "  Albany: (-35.0269°, 117.8837°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1654.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 38124.51 km²",
      "FINAL ANSWER: Area: 38124.51 km², Perimeter: 1654.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 18.56286,
        "lon": 103.72671,
        "name": "Borikhan"
      },
      {
        "lat": 22.35099,
        "lon": 114.20056,
        "name": "Tsz Ching Estate"
      },
      {
        "lat": 14.81667,
        "lon": 120.86667,
        "name": "Balagtas"
      }
    ],
    "ground_truth": {
      "area_km2": 597771.49,
      "perimeter_km": 4133.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Borikhan: (18.5629°, 103.7267°)",
      "  Tsz Ching Estate: (22.3510°, 114.2006°)",
      "  Balagtas: (14.8167°, 120.8667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4133.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 597771.49 km²",
      "FINAL ANSWER: Area: 597771.49 km², Perimeter: 4133.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 53.50291,
        "lon": -1.3458,
        "name": "Wath upon Dearne"
      },
      {
        "lat": 51.13403,
        "lon": 7.59075,
        "name": "Kierspe"
      },
      {
        "lat": 47.79926,
        "lon": 22.86255,
        "name": "Satu Mare"
      },
      {
        "lat": 45.71667,
        "lon": 24.15,
        "name": "Cisnădie"
      }
    ],
    "ground_truth": {
      "area_km2": 234029.22,
      "perimeter_km": 4090.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wath upon Dearne: (53.5029°, -1.3458°)",
      "  Kierspe: (51.1340°, 7.5907°)",
      "  Satu Mare: (47.7993°, 22.8625°)",
      "  Cisnădie: (45.7167°, 24.1500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4090.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 234029.22 km²",
      "FINAL ANSWER: Area: 234029.22 km², Perimeter: 4090.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.88461,
        "lon": 145.29539,
        "name": "Ferntree Gully"
      },
      {
        "lat": -27.10876,
        "lon": 152.94907,
        "name": "Morayfield"
      },
      {
        "lat": -27.91828,
        "lon": 153.33275,
        "name": "Helensvale"
      },
      {
        "lat": -33.82346,
        "lon": 150.94607,
        "name": "Greystanes"
      }
    ],
    "ground_truth": {
      "area_km2": 161624.81,
      "perimeter_km": 2868.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ferntree Gully: (-37.8846°, 145.2954°)",
      "  Morayfield: (-27.1088°, 152.9491°)",
      "  Helensvale: (-27.9183°, 153.3328°)",
      "  Greystanes: (-33.8235°, 150.9461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2868.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 161624.81 km²",
      "FINAL ANSWER: Area: 161624.81 km², Perimeter: 2868.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -2.70924,
        "lon": -80.24719,
        "name": "Posorja"
      },
      {
        "lat": 4.17061,
        "lon": -76.16641,
        "name": "Andalucía"
      },
      {
        "lat": 6.98789,
        "lon": -73.04953,
        "name": "Piedecuesta"
      },
      {
        "lat": 9.4751,
        "lon": -70.73493,
        "name": "El Dividive"
      },
      {
        "lat": 10.15847,
        "lon": -69.00782,
        "name": "Urachiche"
      }
    ],
    "ground_truth": {
      "area_km2": 173036.19,
      "perimeter_km": 3831.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Posorja: (-2.7092°, -80.2472°)",
      "  Andalucía: (4.1706°, -76.1664°)",
      "  Piedecuesta: (6.9879°, -73.0495°)",
      "  El Dividive: (9.4751°, -70.7349°)",
      "  Urachiche: (10.1585°, -69.0078°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3831.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 173036.19 km²",
      "FINAL ANSWER: Area: 173036.19 km², Perimeter: 3831.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.39003,
        "lon": -3.66787,
        "name": "San Diego"
      },
      {
        "lat": 38.76698,
        "lon": -9.29793,
        "name": "Cacém"
      },
      {
        "lat": 42.795,
        "lon": -8.548,
        "name": "Teo"
      },
      {
        "lat": 55.17719,
        "lon": -1.56412,
        "name": "Ashington"
      },
      {
        "lat": 51.25182,
        "lon": 9.40747,
        "name": "Baunatal"
      },
      {
        "lat": 43.33573,
        "lon": 5.48201,
        "name": "Allauch"
      }
    ],
    "ground_truth": {
      "area_km2": 1415908.83,
      "perimeter_km": 5036.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  San Diego: (40.3900°, -3.6679°)",
      "  Cacém: (38.7670°, -9.2979°)",
      "  Teo: (42.7950°, -8.5480°)",
      "  Ashington: (55.1772°, -1.5641°)",
      "  Baunatal: (51.2518°, 9.4075°)",
      "  Allauch: (43.3357°, 5.4820°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5036.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1415908.83 km²",
      "FINAL ANSWER: Area: 1415908.83 km², Perimeter: 5036.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 15.53221,
        "lon": -89.33111,
        "name": "El Estor"
      },
      {
        "lat": 31.56017,
        "lon": -91.40329,
        "name": "Natchez"
      },
      {
        "lat": 41.63031,
        "lon": -87.85394,
        "name": "Orland Park"
      },
      {
        "lat": 27.83975,
        "lon": -82.79121,
        "name": "Seminole"
      },
      {
        "lat": 18.40411,
        "lon": -66.20878,
        "name": "Candelaria"
      }
    ],
    "ground_truth": {
      "area_km2": 2786219.89,
      "perimeter_km": 9027.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  El Estor: (15.5322°, -89.3311°)",
      "  Natchez: (31.5602°, -91.4033°)",
      "  Orland Park: (41.6303°, -87.8539°)",
      "  Seminole: (27.8397°, -82.7912°)",
      "  Candelaria: (18.4041°, -66.2088°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 9027.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2786219.89 km²",
      "FINAL ANSWER: Area: 2786219.89 km², Perimeter: 9027.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.82319,
        "lon": 1.9541,
        "name": "Plaisir"
      },
      {
        "lat": 51.495,
        "lon": 4.29167,
        "name": "Bergen op Zoom"
      },
      {
        "lat": 59.38,
        "lon": 17.80867,
        "name": "Hässelby Villastad"
      },
      {
        "lat": 52.63598,
        "lon": 13.20419,
        "name": "Hennigsdorf"
      },
      {
        "lat": 48.42432,
        "lon": 10.87273,
        "name": "Gersthofen"
      }
    ],
    "ground_truth": {
      "area_km2": 457156.16,
      "perimeter_km": 3514.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Plaisir: (48.8232°, 1.9541°)",
      "  Bergen op Zoom: (51.4950°, 4.2917°)",
      "  Hässelby Villastad: (59.3800°, 17.8087°)",
      "  Hennigsdorf: (52.6360°, 13.2042°)",
      "  Gersthofen: (48.4243°, 10.8727°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3514.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 457156.16 km²",
      "FINAL ANSWER: Area: 457156.16 km², Perimeter: 3514.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 24.08954,
        "lon": 38.0618,
        "name": "Yanbu"
      },
      {
        "lat": 33.01809,
        "lon": 36.12828,
        "name": "Inkhil"
      },
      {
        "lat": 36.26877,
        "lon": 50.0041,
        "name": "Qazvin"
      }
    ],
    "ground_truth": {
      "area_km2": 663357.52,
      "perimeter_km": 4101.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Yanbu: (24.0895°, 38.0618°)",
      "  Inkhil: (33.0181°, 36.1283°)",
      "  Qazvin: (36.2688°, 50.0041°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4101.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 663357.52 km²",
      "FINAL ANSWER: Area: 663357.52 km², Perimeter: 4101.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -22.26257,
        "lon": 166.56621,
        "name": "Mont-Dore"
      },
      {
        "lat": -37.68611,
        "lon": 176.16667,
        "name": "Tauranga"
      },
      {
        "lat": -36.88012,
        "lon": 174.61975,
        "name": "Henderson"
      },
      {
        "lat": -43.53333,
        "lon": 172.63333,
        "name": "Christchurch"
      }
    ],
    "ground_truth": {
      "area_km2": 515755.39,
      "perimeter_km": 5298.31,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mont-Dore: (-22.2626°, 166.5662°)",
      "  Tauranga: (-37.6861°, 176.1667°)",
      "  Henderson: (-36.8801°, 174.6198°)",
      "  Christchurch: (-43.5333°, 172.6333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5298.31 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 515755.39 km²",
      "FINAL ANSWER: Area: 515755.39 km², Perimeter: 5298.31 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.64042,
        "lon": -8.46875,
        "name": "Oulad Barhil"
      },
      {
        "lat": 31.6008,
        "lon": -7.98653,
        "name": "Méchouar-Kasba"
      },
      {
        "lat": 31.83532,
        "lon": -7.31431,
        "name": "Laâttaouia"
      },
      {
        "lat": 36.44788,
        "lon": 8.4413,
        "name": "Ghardimaou"
      },
      {
        "lat": 36.83408,
        "lon": 10.04057,
        "name": "Oued Lill"
      }
    ],
    "ground_truth": {
      "area_km2": 62554.62,
      "perimeter_km": 3710.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Oulad Barhil: (30.6404°, -8.4688°)",
      "  Méchouar-Kasba: (31.6008°, -7.9865°)",
      "  Laâttaouia: (31.8353°, -7.3143°)",
      "  Ghardimaou: (36.4479°, 8.4413°)",
      "  Oued Lill: (36.8341°, 10.0406°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3710.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 62554.62 km²",
      "FINAL ANSWER: Area: 62554.62 km², Perimeter: 3710.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.93333,
        "lon": 145.23333,
        "name": "Rowville"
      },
      {
        "lat": -37.57742,
        "lon": 144.72607,
        "name": "Sunbury"
      },
      {
        "lat": -25.54073,
        "lon": 152.70493,
        "name": "Maryborough"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.8188,
        "lon": 151.1062,
        "name": "Ryde"
      }
    ],
    "ground_truth": {
      "area_km2": 247173.93,
      "perimeter_km": 3227.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rowville: (-37.9333°, 145.2333°)",
      "  Sunbury: (-37.5774°, 144.7261°)",
      "  Maryborough: (-25.5407°, 152.7049°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Ryde: (-33.8188°, 151.1062°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3227.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 247173.93 km²",
      "FINAL ANSWER: Area: 247173.93 km², Perimeter: 3227.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.1009,
        "lon": 6.81411,
        "name": "Elele"
      },
      {
        "lat": 8.43497,
        "lon": 12.05107,
        "name": "Ganye"
      },
      {
        "lat": 8.939,
        "lon": 4.78227,
        "name": "Bode Saadu"
      },
      {
        "lat": 10.26858,
        "lon": 13.26701,
        "name": "Mubi"
      },
      {
        "lat": 12.99809,
        "lon": 15.73195,
        "name": "Massakory"
      },
      {
        "lat": 9.59525,
        "lon": 28.43493,
        "name": "Abyei"
      }
    ],
    "ground_truth": {
      "area_km2": 1199212.38,
      "perimeter_km": 6705.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Elele: (5.1009°, 6.8141°)",
      "  Ganye: (8.4350°, 12.0511°)",
      "  Bode Saadu: (8.9390°, 4.7823°)",
      "  Mubi: (10.2686°, 13.2670°)",
      "  Massakory: (12.9981°, 15.7319°)",
      "  Abyei: (9.5953°, 28.4349°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6705.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1199212.38 km²",
      "FINAL ANSWER: Area: 1199212.38 km², Perimeter: 6705.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.40648,
        "lon": -87.00553,
        "name": "Midway"
      },
      {
        "lat": 37.97476,
        "lon": -87.55585,
        "name": "Evansville"
      },
      {
        "lat": 43.13339,
        "lon": -80.7497,
        "name": "Woodstock"
      },
      {
        "lat": 42.90395,
        "lon": -78.69225,
        "name": "Depew"
      },
      {
        "lat": 40.33813,
        "lon": -79.97894,
        "name": "Baldwin"
      }
    ],
    "ground_truth": {
      "area_km2": 414614.06,
      "perimeter_km": 3402.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Midway: (30.4065°, -87.0055°)",
      "  Evansville: (37.9748°, -87.5559°)",
      "  Woodstock: (43.1334°, -80.7497°)",
      "  Depew: (42.9040°, -78.6923°)",
      "  Baldwin: (40.3381°, -79.9789°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3402.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 414614.06 km²",
      "FINAL ANSWER: Area: 414614.06 km², Perimeter: 3402.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.96491,
        "lon": 23.66511,
        "name": "Agios Ioannis Rentis"
      },
      {
        "lat": 48.33249,
        "lon": 19.66708,
        "name": "Lučenec"
      },
      {
        "lat": 48.73049,
        "lon": 37.58793,
        "name": "Kramatorsk"
      },
      {
        "lat": 48.62831,
        "lon": 38.56205,
        "name": "Pervomaisk"
      }
    ],
    "ground_truth": {
      "area_km2": 829828.51,
      "perimeter_km": 4272.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Agios Ioannis Rentis: (37.9649°, 23.6651°)",
      "  Lučenec: (48.3325°, 19.6671°)",
      "  Kramatorsk: (48.7305°, 37.5879°)",
      "  Pervomaisk: (48.6283°, 38.5620°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4272.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 829828.51 km²",
      "FINAL ANSWER: Area: 829828.51 km², Perimeter: 4272.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -38.26667,
        "lon": 145.01667,
        "name": "Mount Martha"
      },
      {
        "lat": -37.74981,
        "lon": 144.9109,
        "name": "Essendon"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -34.75705,
        "lon": 138.60819,
        "name": "Paralowie"
      },
      {
        "lat": -27.98941,
        "lon": 153.33633,
        "name": "Nerang"
      },
      {
        "lat": -33.92399,
        "lon": 151.22749,
        "name": "Kingsford"
      }
    ],
    "ground_truth": {
      "area_km2": 673920.7,
      "perimeter_km": 3827.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mount Martha: (-38.2667°, 145.0167°)",
      "  Essendon: (-37.7498°, 144.9109°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Paralowie: (-34.7570°, 138.6082°)",
      "  Nerang: (-27.9894°, 153.3363°)",
      "  Kingsford: (-33.9240°, 151.2275°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3827.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 673920.70 km²",
      "FINAL ANSWER: Area: 673920.70 km², Perimeter: 3827.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 4.74851,
        "lon": -6.6363,
        "name": "San-Pédro"
      },
      {
        "lat": 14.79032,
        "lon": -15.90803,
        "name": "Mbaké"
      },
      {
        "lat": 15.85615,
        "lon": -5.79067,
        "name": "Mbera"
      },
      {
        "lat": 12.9591,
        "lon": -2.26075,
        "name": "Yako"
      },
      {
        "lat": 12.25162,
        "lon": -0.42565,
        "name": "Pouytenga"
      },
      {
        "lat": 6.17146,
        "lon": 7.00525,
        "name": "Enugu-Ukwu"
      }
    ],
    "ground_truth": {
      "area_km2": 1604992.09,
      "perimeter_km": 5889.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  San-Pédro: (4.7485°, -6.6363°)",
      "  Mbaké: (14.7903°, -15.9080°)",
      "  Mbera: (15.8561°, -5.7907°)",
      "  Yako: (12.9591°, -2.2607°)",
      "  Pouytenga: (12.2516°, -0.4256°)",
      "  Enugu-Ukwu: (6.1715°, 7.0053°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5889.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1604992.09 km²",
      "FINAL ANSWER: Area: 1604992.09 km², Perimeter: 5889.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -16.7444,
        "lon": 14.97494,
        "name": "Xangongo"
      },
      {
        "lat": -12.35426,
        "lon": 14.77232,
        "name": "Balombo"
      },
      {
        "lat": -6.05255,
        "lon": 26.9143,
        "name": "Kabalo"
      },
      {
        "lat": -16.28333,
        "lon": 27.48333,
        "name": "Monze"
      },
      {
        "lat": -17.93285,
        "lon": 25.83066,
        "name": "Victoria Falls"
      }
    ],
    "ground_truth": {
      "area_km2": 1217577.44,
      "perimeter_km": 4546.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Xangongo: (-16.7444°, 14.9749°)",
      "  Balombo: (-12.3543°, 14.7723°)",
      "  Kabalo: (-6.0526°, 26.9143°)",
      "  Monze: (-16.2833°, 27.4833°)",
      "  Victoria Falls: (-17.9328°, 25.8307°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4546.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1217577.44 km²",
      "FINAL ANSWER: Area: 1217577.44 km², Perimeter: 4546.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.47665,
        "lon": -3.66852,
        "name": "Costillares"
      },
      {
        "lat": 53.4115,
        "lon": -2.83935,
        "name": "Huyton"
      },
      {
        "lat": 52.08362,
        "lon": 15.62513,
        "name": "Sulechów"
      },
      {
        "lat": 51.05305,
        "lon": 13.79831,
        "name": "Blasewitz"
      },
      {
        "lat": 55.71667,
        "lon": 37.41667,
        "name": "Bol’shaya Setun’"
      }
    ],
    "ground_truth": {
      "area_km2": 1105245.31,
      "perimeter_km": 7919.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Costillares: (40.4766°, -3.6685°)",
      "  Huyton: (53.4115°, -2.8394°)",
      "  Sulechów: (52.0836°, 15.6251°)",
      "  Blasewitz: (51.0530°, 13.7983°)",
      "  Bol’shaya Setun’: (55.7167°, 37.4167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7919.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1105245.31 km²",
      "FINAL ANSWER: Area: 1105245.31 km², Perimeter: 7919.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -21.96917,
        "lon": -46.79806,
        "name": "São João da Boa Vista"
      },
      {
        "lat": -25.44472,
        "lon": -49.1925,
        "name": "Pinhais"
      },
      {
        "lat": -20.21111,
        "lon": -50.92583,
        "name": "Santa Fé do Sul"
      },
      {
        "lat": -7.93333,
        "lon": -39.29583,
        "name": "Serrita"
      },
      {
        "lat": -17.21861,
        "lon": -42.59028,
        "name": "Minas Novas"
      },
      {
        "lat": -20.54139,
        "lon": -44.635,
        "name": "Carmópolis de Minas"
      }
    ],
    "ground_truth": {
      "area_km2": 672532.13,
      "perimeter_km": 4711.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  São João da Boa Vista: (-21.9692°, -46.7981°)",
      "  Pinhais: (-25.4447°, -49.1925°)",
      "  Santa Fé do Sul: (-20.2111°, -50.9258°)",
      "  Serrita: (-7.9333°, -39.2958°)",
      "  Minas Novas: (-17.2186°, -42.5903°)",
      "  Carmópolis de Minas: (-20.5414°, -44.6350°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4711.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 672532.13 km²",
      "FINAL ANSWER: Area: 672532.13 km², Perimeter: 4711.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.8,
        "lon": 144.9,
        "name": "Footscray"
      },
      {
        "lat": -27.63917,
        "lon": 153.10944,
        "name": "Logan City"
      },
      {
        "lat": -33.92399,
        "lon": 151.22749,
        "name": "Kingsford"
      }
    ],
    "ground_truth": {
      "area_km2": 152862.71,
      "perimeter_km": 2800.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Footscray: (-37.8000°, 144.9000°)",
      "  Logan City: (-27.6392°, 153.1094°)",
      "  Kingsford: (-33.9240°, 151.2275°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2800.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 152862.71 km²",
      "FINAL ANSWER: Area: 152862.71 km², Perimeter: 2800.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 50.93182,
        "lon": 6.99469,
        "name": "Humboldtkolonie"
      },
      {
        "lat": 53.5476,
        "lon": 8.10395,
        "name": "Wilhelmshaven"
      },
      {
        "lat": 53.86639,
        "lon": 34.44778,
        "name": "Lyudinovo"
      },
      {
        "lat": 48.51716,
        "lon": 34.60617,
        "name": "Kamyanske"
      },
      {
        "lat": 46.81601,
        "lon": 33.47862,
        "name": "Kakhovka"
      }
    ],
    "ground_truth": {
      "area_km2": 1002581.71,
      "perimeter_km": 4805.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Humboldtkolonie: (50.9318°, 6.9947°)",
      "  Wilhelmshaven: (53.5476°, 8.1039°)",
      "  Lyudinovo: (53.8664°, 34.4478°)",
      "  Kamyanske: (48.5172°, 34.6062°)",
      "  Kakhovka: (46.8160°, 33.4786°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4805.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1002581.71 km²",
      "FINAL ANSWER: Area: 1002581.71 km², Perimeter: 4805.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.26224,
        "lon": -9.50377,
        "name": "Ben Jerrar"
      },
      {
        "lat": 33.34499,
        "lon": -3.70387,
        "name": "Outat Oulad Al Haj"
      },
      {
        "lat": 36.78567,
        "lon": 4.06273,
        "name": "Makouda"
      },
      {
        "lat": 36.75472,
        "lon": 6.2725,
        "name": "El Milia"
      },
      {
        "lat": 26.52161,
        "lon": 13.01072,
        "name": "Al Ghurayfah"
      }
    ],
    "ground_truth": {
      "area_km2": 1123258.36,
      "perimeter_km": 5187.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ben Jerrar: (30.2622°, -9.5038°)",
      "  Outat Oulad Al Haj: (33.3450°, -3.7039°)",
      "  Makouda: (36.7857°, 4.0627°)",
      "  El Milia: (36.7547°, 6.2725°)",
      "  Al Ghurayfah: (26.5216°, 13.0107°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5187.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1123258.36 km²",
      "FINAL ANSWER: Area: 1123258.36 km², Perimeter: 5187.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 8.13373,
        "lon": 4.24014,
        "name": "Ogbomoso"
      },
      {
        "lat": 6.76051,
        "lon": -1.59402,
        "name": "Ahwiaa"
      },
      {
        "lat": 11.13417,
        "lon": 2.93861,
        "name": "Kandi"
      },
      {
        "lat": 12.47554,
        "lon": 15.43647,
        "name": "Massaguet"
      },
      {
        "lat": 10.28969,
        "lon": 11.16729,
        "name": "Gombe"
      }
    ],
    "ground_truth": {
      "area_km2": 398243.2,
      "perimeter_km": 4047.47,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ogbomoso: (8.1337°, 4.2401°)",
      "  Ahwiaa: (6.7605°, -1.5940°)",
      "  Kandi: (11.1342°, 2.9386°)",
      "  Massaguet: (12.4755°, 15.4365°)",
      "  Gombe: (10.2897°, 11.1673°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4047.47 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 398243.20 km²",
      "FINAL ANSWER: Area: 398243.20 km², Perimeter: 4047.47 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 145.0,
        "name": "Northcote"
      },
      {
        "lat": -34.75705,
        "lon": 138.60819,
        "name": "Paralowie"
      },
      {
        "lat": -28.21901,
        "lon": 152.03438,
        "name": "Warwick"
      },
      {
        "lat": -27.3171,
        "lon": 153.03097,
        "name": "Bracken Ridge"
      },
      {
        "lat": -33.77271,
        "lon": 151.08184,
        "name": "Epping"
      },
      {
        "lat": -34.4279,
        "lon": 150.89268,
        "name": "Wollongong city centre"
      }
    ],
    "ground_truth": {
      "area_km2": 599307.54,
      "perimeter_km": 3730.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Northcote: (-37.7667°, 145.0000°)",
      "  Paralowie: (-34.7570°, 138.6082°)",
      "  Warwick: (-28.2190°, 152.0344°)",
      "  Bracken Ridge: (-27.3171°, 153.0310°)",
      "  Epping: (-33.7727°, 151.0818°)",
      "  Wollongong city centre: (-34.4279°, 150.8927°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3730.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 599307.54 km²",
      "FINAL ANSWER: Area: 599307.54 km², Perimeter: 3730.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -16.02511,
        "lon": -48.07121,
        "name": "Gama"
      },
      {
        "lat": -2.88,
        "lon": -52.01,
        "name": "Vitória do Xingu"
      },
      {
        "lat": -1.74833,
        "lon": -52.23833,
        "name": "Porto de Moz"
      },
      {
        "lat": -5.61278,
        "lon": -38.76694,
        "name": "Jaguaretama"
      },
      {
        "lat": -7.64265,
        "lon": -47.21738,
        "name": "Santa Luzia"
      }
    ],
    "ground_truth": {
      "area_km2": 1525527.83,
      "perimeter_km": 5104.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gama: (-16.0251°, -48.0712°)",
      "  Vitória do Xingu: (-2.8800°, -52.0100°)",
      "  Porto de Moz: (-1.7483°, -52.2383°)",
      "  Jaguaretama: (-5.6128°, -38.7669°)",
      "  Santa Luzia: (-7.6426°, -47.2174°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5104.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1525527.83 km²",
      "FINAL ANSWER: Area: 1525527.83 km², Perimeter: 5104.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 30.89315,
        "lon": 49.40787,
        "name": "Rāmshīr"
      },
      {
        "lat": 37.41853,
        "lon": 66.04358,
        "name": "Qarqīn"
      },
      {
        "lat": 21.32855,
        "lon": 71.02645,
        "name": "Dhāri"
      }
    ],
    "ground_truth": {
      "area_km2": 1579811.76,
      "perimeter_km": 5943.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Rāmshīr: (30.8931°, 49.4079°)",
      "  Qarqīn: (37.4185°, 66.0436°)",
      "  Dhāri: (21.3285°, 71.0264°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5943.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1579811.76 km²",
      "FINAL ANSWER: Area: 1579811.76 km², Perimeter: 5943.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -9.3,
        "lon": 32.76667,
        "name": "Tunduma"
      },
      {
        "lat": -2.63778,
        "lon": 31.76694,
        "name": "Chato"
      },
      {
        "lat": -3.0804,
        "lon": 29.391,
        "name": "Bubanza"
      },
      {
        "lat": 1.43139,
        "lon": 33.77722,
        "name": "Ngora"
      },
      {
        "lat": 10.45,
        "lon": 38.2,
        "name": "Bichena"
      }
    ],
    "ground_truth": {
      "area_km2": 600333.33,
      "perimeter_km": 5109.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tunduma: (-9.3000°, 32.7667°)",
      "  Chato: (-2.6378°, 31.7669°)",
      "  Bubanza: (-3.0804°, 29.3910°)",
      "  Ngora: (1.4314°, 33.7772°)",
      "  Bichena: (10.4500°, 38.2000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5109.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 600333.33 km²",
      "FINAL ANSWER: Area: 600333.33 km², Perimeter: 5109.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 35.94204,
        "lon": -95.88332,
        "name": "Bixby"
      },
      {
        "lat": 41.6764,
        "lon": -91.58045,
        "name": "Coralville"
      },
      {
        "lat": 42.93173,
        "lon": -76.56605,
        "name": "Auburn"
      },
      {
        "lat": 40.40816,
        "lon": -74.35432,
        "name": "South Old Bridge"
      },
      {
        "lat": 39.65287,
        "lon": -78.76252,
        "name": "Cumberland"
      },
      {
        "lat": 36.09986,
        "lon": -80.24422,
        "name": "Winston-Salem"
      }
    ],
    "ground_truth": {
      "area_km2": 941363.77,
      "perimeter_km": 4520.25,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Bixby: (35.9420°, -95.8833°)",
      "  Coralville: (41.6764°, -91.5804°)",
      "  Auburn: (42.9317°, -76.5661°)",
      "  South Old Bridge: (40.4082°, -74.3543°)",
      "  Cumberland: (39.6529°, -78.7625°)",
      "  Winston-Salem: (36.0999°, -80.2442°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4520.25 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 941363.77 km²",
      "FINAL ANSWER: Area: 941363.77 km², Perimeter: 4520.25 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 31.73443,
        "lon": -7.00505,
        "name": "Demnate"
      },
      {
        "lat": 34.89638,
        "lon": 3.48543,
        "name": "Dar Chioukh"
      },
      {
        "lat": 36.13516,
        "lon": 2.91085,
        "name": "Berrouaghia"
      },
      {
        "lat": 35.85451,
        "lon": 5.29053,
        "name": "Salah Bey"
      },
      {
        "lat": 36.89479,
        "lon": 10.18604,
        "name": "La Gazelle"
      },
      {
        "lat": 34.3827,
        "lon": 8.15549,
        "name": "Ar Rudayyif"
      }
    ],
    "ground_truth": {
      "area_km2": 333200.54,
      "perimeter_km": 3628.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Demnate: (31.7344°, -7.0050°)",
      "  Dar Chioukh: (34.8964°, 3.4854°)",
      "  Berrouaghia: (36.1352°, 2.9108°)",
      "  Salah Bey: (35.8545°, 5.2905°)",
      "  La Gazelle: (36.8948°, 10.1860°)",
      "  Ar Rudayyif: (34.3827°, 8.1555°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3628.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 333200.54 km²",
      "FINAL ANSWER: Area: 333200.54 km², Perimeter: 3628.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.19528,
        "lon": 146.5415,
        "name": "Traralgon"
      },
      {
        "lat": -37.87709,
        "lon": 145.12939,
        "name": "Mount Waverley"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -34.75155,
        "lon": 149.72086,
        "name": "Goulburn"
      }
    ],
    "ground_truth": {
      "area_km2": 53311.44,
      "perimeter_km": 1699.0,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Traralgon: (-38.1953°, 146.5415°)",
      "  Mount Waverley: (-37.8771°, 145.1294°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Goulburn: (-34.7516°, 149.7209°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1699.00 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 53311.44 km²",
      "FINAL ANSWER: Area: 53311.44 km², Perimeter: 1699.00 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -19.8,
        "lon": -41.43833,
        "name": "Mutum"
      },
      {
        "lat": -3.54306,
        "lon": -43.91583,
        "name": "Vargem Grande"
      },
      {
        "lat": -10.83444,
        "lon": -38.53583,
        "name": "Ribeira do Pombal"
      }
    ],
    "ground_truth": {
      "area_km2": 425409.61,
      "perimeter_km": 3876.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mutum: (-19.8000°, -41.4383°)",
      "  Vargem Grande: (-3.5431°, -43.9158°)",
      "  Ribeira do Pombal: (-10.8344°, -38.5358°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3876.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 425409.61 km²",
      "FINAL ANSWER: Area: 425409.61 km², Perimeter: 3876.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.21807,
        "lon": 28.3665,
        "name": "Muğla"
      },
      {
        "lat": 40.89105,
        "lon": 26.90201,
        "name": "Malkara"
      },
      {
        "lat": 39.20762,
        "lon": 46.40678,
        "name": "Kapan"
      },
      {
        "lat": 36.68489,
        "lon": 52.51917,
        "name": "Fereydūn Kenār"
      }
    ],
    "ground_truth": {
      "area_km2": 569455.65,
      "perimeter_km": 4840.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Muğla: (37.2181°, 28.3665°)",
      "  Malkara: (40.8910°, 26.9020°)",
      "  Kapan: (39.2076°, 46.4068°)",
      "  Fereydūn Kenār: (36.6849°, 52.5192°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4840.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 569455.65 km²",
      "FINAL ANSWER: Area: 569455.65 km², Perimeter: 4840.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 45.07176,
        "lon": 7.67919,
        "name": "Centro"
      },
      {
        "lat": 50.704,
        "lon": 7.054,
        "name": "Bonn Hardtberg"
      },
      {
        "lat": 47.88238,
        "lon": 10.62192,
        "name": "Kaufbeuren"
      },
      {
        "lat": 38.22008,
        "lon": 15.24023,
        "name": "Milazzo"
      }
    ],
    "ground_truth": {
      "area_km2": 261272.77,
      "perimeter_km": 3158.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Centro: (45.0718°, 7.6792°)",
      "  Bonn Hardtberg: (50.7040°, 7.0540°)",
      "  Kaufbeuren: (47.8824°, 10.6219°)",
      "  Milazzo: (38.2201°, 15.2402°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3158.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 261272.77 km²",
      "FINAL ANSWER: Area: 261272.77 km², Perimeter: 3158.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 36.97412,
        "lon": -122.0308,
        "name": "Santa Cruz"
      },
      {
        "lat": 37.34772,
        "lon": -120.60908,
        "name": "Atwater"
      },
      {
        "lat": 39.92054,
        "lon": -105.08665,
        "name": "Broomfield"
      }
    ],
    "ground_truth": {
      "area_km2": 1675.77,
      "perimeter_km": 3018.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Santa Cruz: (36.9741°, -122.0308°)",
      "  Atwater: (37.3477°, -120.6091°)",
      "  Broomfield: (39.9205°, -105.0867°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3018.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1675.77 km²",
      "FINAL ANSWER: Area: 1675.77 km², Perimeter: 3018.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -41.51603,
        "lon": 173.9528,
        "name": "Blenheim"
      },
      {
        "lat": -39.06667,
        "lon": 174.08333,
        "name": "New Plymouth"
      },
      {
        "lat": -36.96807,
        "lon": 174.79875,
        "name": "Mangere"
      }
    ],
    "ground_truth": {
      "area_km2": 7395.31,
      "perimeter_km": 1025.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Blenheim: (-41.5160°, 173.9528°)",
      "  New Plymouth: (-39.0667°, 174.0833°)",
      "  Mangere: (-36.9681°, 174.7988°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1025.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 7395.31 km²",
      "FINAL ANSWER: Area: 7395.31 km², Perimeter: 1025.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 17.7,
        "lon": 83.21667,
        "name": "Gajuwaka"
      },
      {
        "lat": 24.33353,
        "lon": 93.66999,
        "name": "Churāchāndpur"
      },
      {
        "lat": 1.36259,
        "lon": 109.30093,
        "name": "Kota Sambas"
      },
      {
        "lat": 7.90963,
        "lon": 98.40248,
        "name": "Ban Ratsada"
      }
    ],
    "ground_truth": {
      "area_km2": 2160935.06,
      "perimeter_km": 7750.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Gajuwaka: (17.7000°, 83.2167°)",
      "  Churāchāndpur: (24.3335°, 93.6700°)",
      "  Kota Sambas: (1.3626°, 109.3009°)",
      "  Ban Ratsada: (7.9096°, 98.4025°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7750.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2160935.06 km²",
      "FINAL ANSWER: Area: 2160935.06 km², Perimeter: 7750.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 46.18096,
        "lon": 6.13921,
        "name": "Carouge"
      },
      {
        "lat": 53.07738,
        "lon": 7.40444,
        "name": "Papenburg"
      },
      {
        "lat": 52.30141,
        "lon": 13.633,
        "name": "Königs Wusterhausen"
      },
      {
        "lat": 52.0814,
        "lon": 21.02397,
        "name": "Piaseczno"
      },
      {
        "lat": 41.68573,
        "lon": 12.77753,
        "name": "Velletri"
      }
    ],
    "ground_truth": {
      "area_km2": 781120.12,
      "perimeter_km": 3746.97,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Carouge: (46.1810°, 6.1392°)",
      "  Papenburg: (53.0774°, 7.4044°)",
      "  Königs Wusterhausen: (52.3014°, 13.6330°)",
      "  Piaseczno: (52.0814°, 21.0240°)",
      "  Velletri: (41.6857°, 12.7775°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3746.97 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 781120.12 km²",
      "FINAL ANSWER: Area: 781120.12 km², Perimeter: 3746.97 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.81819,
        "lon": 145.00176,
        "name": "Richmond"
      },
      {
        "lat": -27.08465,
        "lon": 152.9511,
        "name": "Caboolture"
      },
      {
        "lat": -27.54333,
        "lon": 153.20287,
        "name": "Capalaba"
      }
    ],
    "ground_truth": {
      "area_km2": 33151.62,
      "perimeter_km": 2837.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Richmond: (-37.8182°, 145.0018°)",
      "  Caboolture: (-27.0846°, 152.9511°)",
      "  Capalaba: (-27.5433°, 153.2029°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2837.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 33151.62 km²",
      "FINAL ANSWER: Area: 33151.62 km², Perimeter: 2837.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -27.31472,
        "lon": -48.55917,
        "name": "Governador Celso Ramos"
      },
      {
        "lat": -27.25806,
        "lon": -49.93389,
        "name": "Pouso Redondo"
      },
      {
        "lat": -22.88333,
        "lon": -43.10361,
        "name": "Niterói"
      }
    ],
    "ground_truth": {
      "area_km2": 34296.98,
      "perimeter_km": 1716.02,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Governador Celso Ramos: (-27.3147°, -48.5592°)",
      "  Pouso Redondo: (-27.2581°, -49.9339°)",
      "  Niterói: (-22.8833°, -43.1036°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1716.02 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 34296.98 km²",
      "FINAL ANSWER: Area: 34296.98 km², Perimeter: 1716.02 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 12.42602,
        "lon": 75.7382,
        "name": "Madikeri"
      },
      {
        "lat": 24.13524,
        "lon": 74.04442,
        "name": "Sālūmbar"
      },
      {
        "lat": 25.69515,
        "lon": 81.92336,
        "name": "Mau Aimma"
      }
    ],
    "ground_truth": {
      "area_km2": 534477.48,
      "perimeter_km": 3738.8,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Madikeri: (12.4260°, 75.7382°)",
      "  Sālūmbar: (24.1352°, 74.0444°)",
      "  Mau Aimma: (25.6952°, 81.9234°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3738.80 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 534477.48 km²",
      "FINAL ANSWER: Area: 534477.48 km², Perimeter: 3738.80 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.88214,
        "lon": 144.98215,
        "name": "Elwood"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -27.58333,
        "lon": 153.1,
        "name": "Eight Mile Plains"
      },
      {
        "lat": -31.91099,
        "lon": 152.45387,
        "name": "Taree"
      },
      {
        "lat": -35.41647,
        "lon": 149.06954,
        "name": "Tuggeranong Administrative District"
      }
    ],
    "ground_truth": {
      "area_km2": 182331.68,
      "perimeter_km": 2909.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Elwood: (-37.8821°, 144.9821°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Eight Mile Plains: (-27.5833°, 153.1000°)",
      "  Taree: (-31.9110°, 152.4539°)",
      "  Tuggeranong Administrative District: (-35.4165°, 149.0695°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2909.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 182331.68 km²",
      "FINAL ANSWER: Area: 182331.68 km², Perimeter: 2909.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -27.50766,
        "lon": -58.55625,
        "name": "San Luis del Palmar"
      },
      {
        "lat": -23.28167,
        "lon": -46.74528,
        "name": "Francisco Morato"
      },
      {
        "lat": -24.52611,
        "lon": -49.94861,
        "name": "Piraí do Sul"
      }
    ],
    "ground_truth": {
      "area_km2": 1612.83,
      "perimeter_km": 2550.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  San Luis del Palmar: (-27.5077°, -58.5562°)",
      "  Francisco Morato: (-23.2817°, -46.7453°)",
      "  Piraí do Sul: (-24.5261°, -49.9486°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2550.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1612.83 km²",
      "FINAL ANSWER: Area: 1612.83 km², Perimeter: 2550.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 16.36491,
        "lon": 77.35863,
        "name": "Shaktinagar"
      },
      {
        "lat": 33.46659,
        "lon": 76.88488,
        "name": "Padam"
      },
      {
        "lat": 38.18867,
        "lon": 77.27075,
        "name": "Zepu"
      },
      {
        "lat": 36.8545,
        "lon": 81.66425,
        "name": "Mugala"
      },
      {
        "lat": 23.37583,
        "lon": 93.65389,
        "name": "Tedim"
      }
    ],
    "ground_truth": {
      "area_km2": 2261899.73,
      "perimeter_km": 6602.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Shaktinagar: (16.3649°, 77.3586°)",
      "  Padam: (33.4666°, 76.8849°)",
      "  Zepu: (38.1887°, 77.2708°)",
      "  Mugala: (36.8545°, 81.6642°)",
      "  Tedim: (23.3758°, 93.6539°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6602.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2261899.73 km²",
      "FINAL ANSWER: Area: 2261899.73 km², Perimeter: 6602.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.96179,
        "lon": -96.82917,
        "name": "Addison"
      },
      {
        "lat": 43.59781,
        "lon": -84.76751,
        "name": "Mount Pleasant"
      },
      {
        "lat": 45.50884,
        "lon": -73.58781,
        "name": "Montréal"
      }
    ],
    "ground_truth": {
      "area_km2": 331768.91,
      "perimeter_km": 4915.64,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Addison: (32.9618°, -96.8292°)",
      "  Mount Pleasant: (43.5978°, -84.7675°)",
      "  Montréal: (45.5088°, -73.5878°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4915.64 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 331768.91 km²",
      "FINAL ANSWER: Area: 331768.91 km², Perimeter: 4915.64 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.5064,
        "lon": 34.92087,
        "name": "Or Akiva"
      },
      {
        "lat": 39.64917,
        "lon": 27.88611,
        "name": "Balıkesir"
      },
      {
        "lat": 40.76499,
        "lon": 29.92928,
        "name": "İzmit"
      },
      {
        "lat": 38.6908,
        "lon": 35.5538,
        "name": "Talas"
      },
      {
        "lat": 40.75972,
        "lon": 36.3225,
        "name": "Taşova"
      },
      {
        "lat": 31.01547,
        "lon": 47.43362,
        "name": "Al Qurnah"
      }
    ],
    "ground_truth": {
      "area_km2": 848641.41,
      "perimeter_km": 4666.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Or Akiva: (32.5064°, 34.9209°)",
      "  Balıkesir: (39.6492°, 27.8861°)",
      "  İzmit: (40.7650°, 29.9293°)",
      "  Talas: (38.6908°, 35.5538°)",
      "  Taşova: (40.7597°, 36.3225°)",
      "  Al Qurnah: (31.0155°, 47.4336°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4666.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 848641.41 km²",
      "FINAL ANSWER: Area: 848641.41 km², Perimeter: 4666.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -34.91119,
        "lon": 138.70735,
        "name": "Adelaide Hills"
      },
      {
        "lat": -33.91938,
        "lon": 150.92588,
        "name": "Liverpool"
      },
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      }
    ],
    "ground_truth": {
      "area_km2": 230727.33,
      "perimeter_km": 2543.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Adelaide Hills: (-34.9112°, 138.7073°)",
      "  Liverpool: (-33.9194°, 150.9259°)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2543.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 230727.33 km²",
      "FINAL ANSWER: Area: 230727.33 km², Perimeter: 2543.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -41.13827,
        "lon": 175.0502,
        "name": "Upper Hutt"
      },
      {
        "lat": -36.88745,
        "lon": 174.77059,
        "name": "Epsom"
      },
      {
        "lat": -37.78821,
        "lon": 175.2902,
        "name": "Hamilton East"
      },
      {
        "lat": -40.95972,
        "lon": 175.6575,
        "name": "Masterton"
      }
    ],
    "ground_truth": {
      "area_km2": 18911.08,
      "perimeter_km": 992.2,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Upper Hutt: (-41.1383°, 175.0502°)",
      "  Epsom: (-36.8875°, 174.7706°)",
      "  Hamilton East: (-37.7882°, 175.2902°)",
      "  Masterton: (-40.9597°, 175.6575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 992.20 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 18911.08 km²",
      "FINAL ANSWER: Area: 18911.08 km², Perimeter: 992.20 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 42.97839,
        "lon": -78.79976,
        "name": "Amherst"
      },
      {
        "lat": 41.66121,
        "lon": -72.77954,
        "name": "New Britain"
      },
      {
        "lat": 40.72149,
        "lon": -73.7693,
        "name": "Terrace Heights"
      }
    ],
    "ground_truth": {
      "area_km2": 32294.24,
      "perimeter_km": 1135.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Amherst: (42.9784°, -78.7998°)",
      "  New Britain: (41.6612°, -72.7795°)",
      "  Terrace Heights: (40.7215°, -73.7693°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1135.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 32294.24 km²",
      "FINAL ANSWER: Area: 32294.24 km², Perimeter: 1135.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -10.98303,
        "lon": 26.7384,
        "name": "Likasi"
      },
      {
        "lat": -4.36667,
        "lon": 35.08333,
        "name": "Basotu"
      },
      {
        "lat": -11.01863,
        "lon": 33.85746,
        "name": "Rumphi"
      }
    ],
    "ground_truth": {
      "area_km2": 287809.36,
      "perimeter_km": 2706.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Likasi: (-10.9830°, 26.7384°)",
      "  Basotu: (-4.3667°, 35.0833°)",
      "  Rumphi: (-11.0186°, 33.8575°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2706.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 287809.36 km²",
      "FINAL ANSWER: Area: 287809.36 km², Perimeter: 2706.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 39.54595,
        "lon": -0.57069,
        "name": "Ribarroja del Turia"
      },
      {
        "lat": 56.33871,
        "lon": -2.79902,
        "name": "Saint Andrews"
      },
      {
        "lat": 52.234,
        "lon": 4.44474,
        "name": "Noordwijk-Binnen"
      },
      {
        "lat": 50.14952,
        "lon": 18.84215,
        "name": "Łaziska Górne"
      },
      {
        "lat": 40.57762,
        "lon": 17.03812,
        "name": "Palagiano"
      }
    ],
    "ground_truth": {
      "area_km2": 1973145.81,
      "perimeter_km": 6130.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ribarroja del Turia: (39.5459°, -0.5707°)",
      "  Saint Andrews: (56.3387°, -2.7990°)",
      "  Noordwijk-Binnen: (52.2340°, 4.4447°)",
      "  Łaziska Górne: (50.1495°, 18.8422°)",
      "  Palagiano: (40.5776°, 17.0381°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6130.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1973145.81 km²",
      "FINAL ANSWER: Area: 1973145.81 km², Perimeter: 6130.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 50.31505,
        "lon": 17.38355,
        "name": "Głuchołazy"
      },
      {
        "lat": 58.14,
        "lon": 52.65619,
        "name": "Glazov"
      },
      {
        "lat": 51.88056,
        "lon": 45.00609,
        "name": "Atkarsk"
      }
    ],
    "ground_truth": {
      "area_km2": 743305.95,
      "perimeter_km": 5192.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Głuchołazy: (50.3150°, 17.3835°)",
      "  Glazov: (58.1400°, 52.6562°)",
      "  Atkarsk: (51.8806°, 45.0061°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5192.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 743305.95 km²",
      "FINAL ANSWER: Area: 743305.95 km², Perimeter: 5192.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -3.54964,
        "lon": 143.63229,
        "name": "Wewak"
      },
      {
        "lat": 13.48773,
        "lon": 144.78138,
        "name": "Tamuning-Tumon-Harmon Village"
      },
      {
        "lat": 15.21233,
        "lon": 145.7545,
        "name": "Saipan"
      },
      {
        "lat": 6.92477,
        "lon": 158.16109,
        "name": "Palikir"
      }
    ],
    "ground_truth": {
      "area_km2": 1634342.25,
      "perimeter_km": 5743.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wewak: (-3.5496°, 143.6323°)",
      "  Tamuning-Tumon-Harmon Village: (13.4877°, 144.7814°)",
      "  Saipan: (15.2123°, 145.7545°)",
      "  Palikir: (6.9248°, 158.1611°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5743.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1634342.25 km²",
      "FINAL ANSWER: Area: 1634342.25 km², Perimeter: 5743.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 4.5141,
        "lon": 103.4483,
        "name": "Kertih"
      },
      {
        "lat": 17.3072,
        "lon": 102.18886,
        "name": "Na Klang"
      },
      {
        "lat": -6.7559,
        "lon": 111.038,
        "name": "Pati"
      },
      {
        "lat": -6.17806,
        "lon": 106.63,
        "name": "Tangerang"
      }
    ],
    "ground_truth": {
      "area_km2": 805351.74,
      "perimeter_km": 6007.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Kertih: (4.5141°, 103.4483°)",
      "  Na Klang: (17.3072°, 102.1889°)",
      "  Pati: (-6.7559°, 111.0380°)",
      "  Tangerang: (-6.1781°, 106.6300°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6007.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 805351.74 km²",
      "FINAL ANSWER: Area: 805351.74 km², Perimeter: 6007.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.71372,
        "lon": -117.76091,
        "name": "Northwood"
      },
      {
        "lat": 34.19731,
        "lon": -118.64398,
        "name": "West Hills"
      },
      {
        "lat": 49.24966,
        "lon": -123.11934,
        "name": "Vancouver"
      },
      {
        "lat": 52.13238,
        "lon": -106.66892,
        "name": "Saskatoon"
      },
      {
        "lat": 33.4356,
        "lon": -112.3496,
        "name": "Avondale"
      }
    ],
    "ground_truth": {
      "area_km2": 1673809.22,
      "perimeter_km": 5641.27,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Northwood: (33.7137°, -117.7609°)",
      "  West Hills: (34.1973°, -118.6440°)",
      "  Vancouver: (49.2497°, -123.1193°)",
      "  Saskatoon: (52.1324°, -106.6689°)",
      "  Avondale: (33.4356°, -112.3496°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5641.27 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1673809.22 km²",
      "FINAL ANSWER: Area: 1673809.22 km², Perimeter: 5641.27 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 10.96209,
        "lon": -3.24967,
        "name": "Diébougou"
      },
      {
        "lat": 11.31755,
        "lon": -5.66654,
        "name": "Sikasso"
      },
      {
        "lat": 10.13366,
        "lon": 14.70748,
        "name": "Guidiguis"
      }
    ],
    "ground_truth": {
      "area_km2": 35723.4,
      "perimeter_km": 4460.84,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Diébougou: (10.9621°, -3.2497°)",
      "  Sikasso: (11.3176°, -5.6665°)",
      "  Guidiguis: (10.1337°, 14.7075°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4460.84 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 35723.40 km²",
      "FINAL ANSWER: Area: 35723.40 km², Perimeter: 4460.84 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 51.2099,
        "lon": 4.03651,
        "name": "Stekene"
      },
      {
        "lat": 51.91917,
        "lon": 5.84167,
        "name": "Elst"
      },
      {
        "lat": 52.11457,
        "lon": 8.67343,
        "name": "Herford"
      },
      {
        "lat": 46.88152,
        "lon": 17.44117,
        "name": "Tapolca"
      },
      {
        "lat": 43.29789,
        "lon": 13.45293,
        "name": "Macerata"
      }
    ],
    "ground_truth": {
      "area_km2": 396884.32,
      "perimeter_km": 2837.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Stekene: (51.2099°, 4.0365°)",
      "  Elst: (51.9192°, 5.8417°)",
      "  Herford: (52.1146°, 8.6734°)",
      "  Tapolca: (46.8815°, 17.4412°)",
      "  Macerata: (43.2979°, 13.4529°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2837.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 396884.32 km²",
      "FINAL ANSWER: Area: 396884.32 km², Perimeter: 2837.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.87045,
        "lon": -1.42319,
        "name": "Beni Mester"
      },
      {
        "lat": 36.10124,
        "lon": 1.19949,
        "name": "Oued Sly"
      },
      {
        "lat": 36.65,
        "lon": 4.77361,
        "name": "el hed"
      },
      {
        "lat": 36.51611,
        "lon": 6.32722,
        "name": "Grarem"
      },
      {
        "lat": 32.63278,
        "lon": 12.87361,
        "name": "An Nāşirīyah"
      },
      {
        "lat": 34.72224,
        "lon": 5.37845,
        "name": "Tolga"
      }
    ],
    "ground_truth": {
      "area_km2": 274570.84,
      "perimeter_km": 2830.08,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Beni Mester: (34.8704°, -1.4232°)",
      "  Oued Sly: (36.1012°, 1.1995°)",
      "  el hed: (36.6500°, 4.7736°)",
      "  Grarem: (36.5161°, 6.3272°)",
      "  An Nāşirīyah: (32.6328°, 12.8736°)",
      "  Tolga: (34.7222°, 5.3784°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2830.08 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 274570.84 km²",
      "FINAL ANSWER: Area: 274570.84 km², Perimeter: 2830.08 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 43.80486,
        "lon": -79.35442,
        "name": "Hillcrest Village"
      },
      {
        "lat": 42.55843,
        "lon": -70.88005,
        "name": "Beverly"
      },
      {
        "lat": 41.34621,
        "lon": -73.079,
        "name": "Ansonia"
      }
    ],
    "ground_truth": {
      "area_km2": 60853.35,
      "perimeter_km": 1508.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hillcrest Village: (43.8049°, -79.3544°)",
      "  Beverly: (42.5584°, -70.8800°)",
      "  Ansonia: (41.3462°, -73.0790°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1508.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 60853.35 km²",
      "FINAL ANSWER: Area: 60853.35 km², Perimeter: 1508.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 48.79266,
        "lon": 2.46569,
        "name": "Créteil"
      },
      {
        "lat": 57.76638,
        "lon": 40.92828,
        "name": "Kostroma"
      },
      {
        "lat": 44.62693,
        "lon": 22.65288,
        "name": "Drobeta-Turnu Severin"
      }
    ],
    "ground_truth": {
      "area_km2": 1542652.66,
      "perimeter_km": 6227.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Créteil: (48.7927°, 2.4657°)",
      "  Kostroma: (57.7664°, 40.9283°)",
      "  Drobeta-Turnu Severin: (44.6269°, 22.6529°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6227.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1542652.66 km²",
      "FINAL ANSWER: Area: 1542652.66 km², Perimeter: 6227.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 21.63333,
        "lon": 108.95,
        "name": "Xichang"
      },
      {
        "lat": 14.95472,
        "lon": 120.89694,
        "name": "Baliuag"
      },
      {
        "lat": 14.11356,
        "lon": 121.55574,
        "name": "Lucban"
      }
    ],
    "ground_truth": {
      "area_km2": 30199.19,
      "perimeter_km": 3153.19,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Xichang: (21.6333°, 108.9500°)",
      "  Baliuag: (14.9547°, 120.8969°)",
      "  Lucban: (14.1136°, 121.5557°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3153.19 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 30199.19 km²",
      "FINAL ANSWER: Area: 30199.19 km², Perimeter: 3153.19 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -28.29389,
        "lon": -49.93167,
        "name": "São Joaquim"
      },
      {
        "lat": -23.20083,
        "lon": -47.28694,
        "name": "Salto"
      },
      {
        "lat": -14.52972,
        "lon": -40.36528,
        "name": "Poções"
      },
      {
        "lat": -12.53556,
        "lon": -39.19083,
        "name": "Cabaceiras do Paraguaçu"
      },
      {
        "lat": -8.87556,
        "lon": -36.36667,
        "name": "São João"
      },
      {
        "lat": -20.12861,
        "lon": -40.30778,
        "name": "Serra"
      }
    ],
    "ground_truth": {
      "area_km2": 549061.19,
      "perimeter_km": 5251.98,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  São Joaquim: (-28.2939°, -49.9317°)",
      "  Salto: (-23.2008°, -47.2869°)",
      "  Poções: (-14.5297°, -40.3653°)",
      "  Cabaceiras do Paraguaçu: (-12.5356°, -39.1908°)",
      "  São João: (-8.8756°, -36.3667°)",
      "  Serra: (-20.1286°, -40.3078°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5251.98 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 549061.19 km²",
      "FINAL ANSWER: Area: 549061.19 km², Perimeter: 5251.98 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -34.5627,
        "lon": -58.45829,
        "name": "Belgrano"
      },
      {
        "lat": -25.44227,
        "lon": -49.06795,
        "name": "Piraquara"
      },
      {
        "lat": -14.06694,
        "lon": -39.64056,
        "name": "Ibirataia"
      },
      {
        "lat": -22.80389,
        "lon": -43.37222,
        "name": "São João de Meriti"
      }
    ],
    "ground_truth": {
      "area_km2": 402760.22,
      "perimeter_km": 5972.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Belgrano: (-34.5627°, -58.4583°)",
      "  Piraquara: (-25.4423°, -49.0680°)",
      "  Ibirataia: (-14.0669°, -39.6406°)",
      "  São João de Meriti: (-22.8039°, -43.3722°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5972.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 402760.22 km²",
      "FINAL ANSWER: Area: 402760.22 km², Perimeter: 5972.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 22.71667,
        "lon": 70.28333,
        "name": "Jodiya Bandar"
      },
      {
        "lat": 38.20835,
        "lon": 67.20664,
        "name": "Boysun"
      },
      {
        "lat": 40.35667,
        "lon": 71.28472,
        "name": "Rishton"
      },
      {
        "lat": 29.10298,
        "lon": 75.17138,
        "name": "Bhādra"
      },
      {
        "lat": 22.59573,
        "lon": 76.9133,
        "name": "Khātegaon"
      }
    ],
    "ground_truth": {
      "area_km2": 1019201.97,
      "perimeter_km": 4896.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Jodiya Bandar: (22.7167°, 70.2833°)",
      "  Boysun: (38.2084°, 67.2066°)",
      "  Rishton: (40.3567°, 71.2847°)",
      "  Bhādra: (29.1030°, 75.1714°)",
      "  Khātegaon: (22.5957°, 76.9133°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4896.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1019201.97 km²",
      "FINAL ANSWER: Area: 1019201.97 km², Perimeter: 4896.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 34.80556,
        "lon": 116.63889,
        "name": "Shizhai"
      },
      {
        "lat": 35.47619,
        "lon": 136.7721,
        "name": "Yamagata"
      },
      {
        "lat": 32.94584,
        "lon": 132.98635,
        "name": "Shimoda"
      }
    ],
    "ground_truth": {
      "area_km2": 271586.21,
      "perimeter_km": 3798.12,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Shizhai: (34.8056°, 116.6389°)",
      "  Yamagata: (35.4762°, 136.7721°)",
      "  Shimoda: (32.9458°, 132.9863°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3798.12 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 271586.21 km²",
      "FINAL ANSWER: Area: 271586.21 km², Perimeter: 3798.12 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.59283,
        "lon": -98.91084,
        "name": "Tezoyuca"
      },
      {
        "lat": 29.77828,
        "lon": -95.17188,
        "name": "Cloverleaf"
      },
      {
        "lat": 27.29393,
        "lon": -80.35033,
        "name": "Port Saint Lucie"
      },
      {
        "lat": 14.30097,
        "lon": -90.78816,
        "name": "Escuintla"
      }
    ],
    "ground_truth": {
      "area_km2": 1819230.45,
      "perimeter_km": 5516.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Tezoyuca: (19.5928°, -98.9108°)",
      "  Cloverleaf: (29.7783°, -95.1719°)",
      "  Port Saint Lucie: (27.2939°, -80.3503°)",
      "  Escuintla: (14.3010°, -90.7882°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5516.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1819230.45 km²",
      "FINAL ANSWER: Area: 1819230.45 km², Perimeter: 5516.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.20554,
        "lon": -46.7838,
        "name": "Campo Limpo Paulista"
      },
      {
        "lat": -22.28306,
        "lon": -46.36889,
        "name": "Ouro Fino"
      },
      {
        "lat": -19.22,
        "lon": -42.48361,
        "name": "Belo Oriente"
      }
    ],
    "ground_truth": {
      "area_km2": 13840.0,
      "perimeter_km": 1267.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Campo Limpo Paulista: (-23.2055°, -46.7838°)",
      "  Ouro Fino: (-22.2831°, -46.3689°)",
      "  Belo Oriente: (-19.2200°, -42.4836°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1267.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 13840.00 km²",
      "FINAL ANSWER: Area: 13840.00 km², Perimeter: 1267.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 19.02681,
        "lon": 74.71487,
        "name": "Ārangaon"
      },
      {
        "lat": 27.56155,
        "lon": 73.47141,
        "name": "Nokha"
      },
      {
        "lat": 31.80921,
        "lon": 75.20294,
        "name": "Batāla"
      },
      {
        "lat": 16.94761,
        "lon": 81.77987,
        "name": "Dowleswaram"
      },
      {
        "lat": 17.93023,
        "lon": 80.82671,
        "name": "Manuguru"
      }
    ],
    "ground_truth": {
      "area_km2": 680540.1,
      "perimeter_km": 4043.9,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Ārangaon: (19.0268°, 74.7149°)",
      "  Nokha: (27.5616°, 73.4714°)",
      "  Batāla: (31.8092°, 75.2029°)",
      "  Dowleswaram: (16.9476°, 81.7799°)",
      "  Manuguru: (17.9302°, 80.8267°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4043.90 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 680540.10 km²",
      "FINAL ANSWER: Area: 680540.10 km², Perimeter: 4043.90 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 17.52333,
        "lon": 80.60405,
        "name": "Chunchupally"
      },
      {
        "lat": 29.41223,
        "lon": 76.9547,
        "name": "Panipat Taraf Ansar"
      },
      {
        "lat": 26.71004,
        "lon": 88.42851,
        "name": "Siliguri"
      },
      {
        "lat": 16.10864,
        "lon": 102.25808,
        "name": "Kaeng Khro"
      }
    ],
    "ground_truth": {
      "area_km2": 1918815.96,
      "perimeter_km": 6698.61,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Chunchupally: (17.5233°, 80.6041°)",
      "  Panipat Taraf Ansar: (29.4122°, 76.9547°)",
      "  Siliguri: (26.7100°, 88.4285°)",
      "  Kaeng Khro: (16.1086°, 102.2581°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6698.61 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1918815.96 km²",
      "FINAL ANSWER: Area: 1918815.96 km², Perimeter: 6698.61 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.79833,
        "lon": 117.86639,
        "name": "Guanshan"
      },
      {
        "lat": 41.79556,
        "lon": 129.77583,
        "name": "Chongjin"
      },
      {
        "lat": 35.17325,
        "lon": 137.05667,
        "name": "Nagakute"
      },
      {
        "lat": 33.35634,
        "lon": 130.74966,
        "name": "Ukiha"
      },
      {
        "lat": 32.65,
        "lon": 130.66667,
        "name": "Matsubase"
      }
    ],
    "ground_truth": {
      "area_km2": 879823.55,
      "perimeter_km": 4230.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Guanshan: (33.7983°, 117.8664°)",
      "  Chongjin: (41.7956°, 129.7758°)",
      "  Nagakute: (35.1733°, 137.0567°)",
      "  Ukiha: (33.3563°, 130.7497°)",
      "  Matsubase: (32.6500°, 130.6667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4230.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 879823.55 km²",
      "FINAL ANSWER: Area: 879823.55 km², Perimeter: 4230.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.18333,
        "lon": 145.08333,
        "name": "Mount Eliza"
      },
      {
        "lat": -27.63917,
        "lon": 153.10944,
        "name": "Logan City"
      },
      {
        "lat": -28.11694,
        "lon": 153.46584,
        "name": "Palm Beach"
      },
      {
        "lat": -33.9125,
        "lon": 151.10279,
        "name": "Campsie"
      }
    ],
    "ground_truth": {
      "area_km2": 152287.19,
      "perimeter_km": 2855.92,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mount Eliza: (-38.1833°, 145.0833°)",
      "  Logan City: (-27.6392°, 153.1094°)",
      "  Palm Beach: (-28.1169°, 153.4658°)",
      "  Campsie: (-33.9125°, 151.1028°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2855.92 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 152287.19 km²",
      "FINAL ANSWER: Area: 152287.19 km², Perimeter: 2855.92 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -36.12179,
        "lon": 146.88809,
        "name": "Wodonga"
      },
      {
        "lat": -37.88333,
        "lon": 145.21667,
        "name": "Wantirna South"
      },
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -27.46794,
        "lon": 153.02809,
        "name": "Brisbane"
      },
      {
        "lat": -33.92598,
        "lon": 151.19347,
        "name": "Mascot"
      }
    ],
    "ground_truth": {
      "area_km2": 189299.75,
      "perimeter_km": 3122.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Wodonga: (-36.1218°, 146.8881°)",
      "  Wantirna South: (-37.8833°, 145.2167°)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Brisbane: (-27.4679°, 153.0281°)",
      "  Mascot: (-33.9260°, 151.1935°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3122.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 189299.75 km²",
      "FINAL ANSWER: Area: 189299.75 km², Perimeter: 3122.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.2,
        "lon": 0.11667,
        "name": "Cambridge"
      },
      {
        "lat": 53.3618,
        "lon": -2.73406,
        "name": "Widnes"
      },
      {
        "lat": 46.21667,
        "lon": 20.48333,
        "name": "Makó"
      }
    ],
    "ground_truth": {
      "area_km2": 60868.09,
      "perimeter_km": 3681.51,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Cambridge: (52.2000°, 0.1167°)",
      "  Widnes: (53.3618°, -2.7341°)",
      "  Makó: (46.2167°, 20.4833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3681.51 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 60868.09 km²",
      "FINAL ANSWER: Area: 60868.09 km², Perimeter: 3681.51 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 144.91667,
        "name": "Moonee Ponds"
      },
      {
        "lat": -27.61025,
        "lon": 153.05388,
        "name": "Sunnybank Hills"
      },
      {
        "lat": -33.89743,
        "lon": 150.93446,
        "name": "Cabramatta"
      }
    ],
    "ground_truth": {
      "area_km2": 138343.13,
      "perimeter_km": 2780.66,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Moonee Ponds: (-37.7667°, 144.9167°)",
      "  Sunnybank Hills: (-27.6103°, 153.0539°)",
      "  Cabramatta: (-33.8974°, 150.9345°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2780.66 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 138343.13 km²",
      "FINAL ANSWER: Area: 138343.13 km², Perimeter: 2780.66 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -31.70312,
        "lon": 27.2329,
        "name": "Lady Frere"
      },
      {
        "lat": -19.45,
        "lon": 29.81667,
        "name": "Gweru"
      },
      {
        "lat": -23.35,
        "lon": 43.66667,
        "name": "Toliara"
      }
    ],
    "ground_truth": {
      "area_km2": 1031850.84,
      "perimeter_km": 4748.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lady Frere: (-31.7031°, 27.2329°)",
      "  Gweru: (-19.4500°, 29.8167°)",
      "  Toliara: (-23.3500°, 43.6667°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4748.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1031850.84 km²",
      "FINAL ANSWER: Area: 1031850.84 km², Perimeter: 4748.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 12.01292,
        "lon": -83.76449,
        "name": "Bluefields"
      },
      {
        "lat": 15.86275,
        "lon": -97.06835,
        "name": "Puerto Escondido"
      },
      {
        "lat": 26.66729,
        "lon": -81.88009,
        "name": "North Fort Myers"
      },
      {
        "lat": 23.0072,
        "lon": -82.4017,
        "name": "Boyeros"
      },
      {
        "lat": 18.41538,
        "lon": -70.03317,
        "name": "Bajos de Haina"
      }
    ],
    "ground_truth": {
      "area_km2": 2049759.06,
      "perimeter_km": 6903.5,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Bluefields: (12.0129°, -83.7645°)",
      "  Puerto Escondido: (15.8628°, -97.0683°)",
      "  North Fort Myers: (26.6673°, -81.8801°)",
      "  Boyeros: (23.0072°, -82.4017°)",
      "  Bajos de Haina: (18.4154°, -70.0332°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6903.50 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2049759.06 km²",
      "FINAL ANSWER: Area: 2049759.06 km², Perimeter: 6903.50 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 35.87687,
        "lon": 14.53592,
        "name": "Żabbar"
      },
      {
        "lat": 44.77879,
        "lon": 17.20629,
        "name": "Banja Luka"
      },
      {
        "lat": 50.95843,
        "lon": 13.93702,
        "name": "Pirna"
      },
      {
        "lat": 49.77984,
        "lon": 18.43688,
        "name": "Havířov"
      },
      {
        "lat": 50.62036,
        "lon": 26.23695,
        "name": "Rivne"
      }
    ],
    "ground_truth": {
      "area_km2": 870553.06,
      "perimeter_km": 4540.26,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Żabbar: (35.8769°, 14.5359°)",
      "  Banja Luka: (44.7788°, 17.2063°)",
      "  Pirna: (50.9584°, 13.9370°)",
      "  Havířov: (49.7798°, 18.4369°)",
      "  Rivne: (50.6204°, 26.2370°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4540.26 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 870553.06 km²",
      "FINAL ANSWER: Area: 870553.06 km², Perimeter: 4540.26 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -24.79889,
        "lon": -53.30667,
        "name": "Corbélia"
      },
      {
        "lat": -16.83056,
        "lon": -49.53194,
        "name": "Guapó"
      },
      {
        "lat": -15.67941,
        "lon": -48.19667,
        "name": "Brazlândia"
      },
      {
        "lat": -2.95528,
        "lon": -44.80694,
        "name": "São João Batista"
      },
      {
        "lat": -22.53722,
        "lon": -42.98194,
        "name": "Guapimirim"
      }
    ],
    "ground_truth": {
      "area_km2": 1394988.28,
      "perimeter_km": 5890.23,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Corbélia: (-24.7989°, -53.3067°)",
      "  Guapó: (-16.8306°, -49.5319°)",
      "  Brazlândia: (-15.6794°, -48.1967°)",
      "  São João Batista: (-2.9553°, -44.8069°)",
      "  Guapimirim: (-22.5372°, -42.9819°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5890.23 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1394988.28 km²",
      "FINAL ANSWER: Area: 1394988.28 km², Perimeter: 5890.23 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -33.79798,
        "lon": 151.28826,
        "name": "Manly"
      },
      {
        "lat": -38.19528,
        "lon": 146.5415,
        "name": "Traralgon"
      },
      {
        "lat": -37.99116,
        "lon": 145.17385,
        "name": "Keysborough"
      },
      {
        "lat": -31.09048,
        "lon": 150.92905,
        "name": "Tamworth"
      },
      {
        "lat": -28.00274,
        "lon": 153.42999,
        "name": "Surfers Paradise"
      },
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      }
    ],
    "ground_truth": {
      "area_km2": 545188.44,
      "perimeter_km": 5536.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Manly: (-33.7980°, 151.2883°)",
      "  Traralgon: (-38.1953°, 146.5415°)",
      "  Keysborough: (-37.9912°, 145.1738°)",
      "  Tamworth: (-31.0905°, 150.9290°)",
      "  Surfers Paradise: (-28.0027°, 153.4300°)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5536.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 545188.44 km²",
      "FINAL ANSWER: Area: 545188.44 km², Perimeter: 5536.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 4.9353,
        "lon": -6.77828,
        "name": "Watté"
      },
      {
        "lat": 10.86225,
        "lon": 0.20762,
        "name": "Dapaong"
      },
      {
        "lat": 12.55,
        "lon": -0.96667,
        "name": "Barogo"
      },
      {
        "lat": 14.3521,
        "lon": 3.3168,
        "name": "Filingué"
      },
      {
        "lat": 10.85009,
        "lon": 8.199,
        "name": "Dutsen Wai"
      },
      {
        "lat": 4.25671,
        "lon": 18.41583,
        "name": "Bimbo"
      }
    ],
    "ground_truth": {
      "area_km2": 1705909.17,
      "perimeter_km": 6538.57,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Watté: (4.9353°, -6.7783°)",
      "  Dapaong: (10.8622°, 0.2076°)",
      "  Barogo: (12.5500°, -0.9667°)",
      "  Filingué: (14.3521°, 3.3168°)",
      "  Dutsen Wai: (10.8501°, 8.1990°)",
      "  Bimbo: (4.2567°, 18.4158°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6538.57 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1705909.17 km²",
      "FINAL ANSWER: Area: 1705909.17 km², Perimeter: 6538.57 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.88247,
        "lon": 16.60086,
        "name": "Catanzaro"
      },
      {
        "lat": 55.93333,
        "lon": 23.31667,
        "name": "Šiauliai"
      },
      {
        "lat": 48.52496,
        "lon": 25.03712,
        "name": "Kolomyia"
      }
    ],
    "ground_truth": {
      "area_km2": 361087.67,
      "perimeter_km": 4058.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Catanzaro: (38.8825°, 16.6009°)",
      "  Šiauliai: (55.9333°, 23.3167°)",
      "  Kolomyia: (48.5250°, 25.0371°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4058.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 361087.67 km²",
      "FINAL ANSWER: Area: 361087.67 km², Perimeter: 4058.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.87029,
        "lon": -117.92534,
        "name": "Fullerton"
      },
      {
        "lat": 40.39162,
        "lon": -111.85077,
        "name": "Lehi"
      },
      {
        "lat": 37.7528,
        "lon": -100.01708,
        "name": "Dodge City"
      },
      {
        "lat": 33.10317,
        "lon": -96.67055,
        "name": "Allen"
      },
      {
        "lat": 31.08351,
        "lon": -97.65974,
        "name": "Harker Heights"
      }
    ],
    "ground_truth": {
      "area_km2": 1134620.66,
      "perimeter_km": 4729.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Fullerton: (33.8703°, -117.9253°)",
      "  Lehi: (40.3916°, -111.8508°)",
      "  Dodge City: (37.7528°, -100.0171°)",
      "  Allen: (33.1032°, -96.6706°)",
      "  Harker Heights: (31.0835°, -97.6597°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4729.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1134620.66 km²",
      "FINAL ANSWER: Area: 1134620.66 km², Perimeter: 4729.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -20.95361,
        "lon": -43.80639,
        "name": "Carandaí"
      },
      {
        "lat": -23.68611,
        "lon": -46.62278,
        "name": "Diadema"
      },
      {
        "lat": -10.685,
        "lon": -37.42528,
        "name": "Itabaiana"
      }
    ],
    "ground_truth": {
      "area_km2": 55098.38,
      "perimeter_km": 3492.83,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Carandaí: (-20.9536°, -43.8064°)",
      "  Diadema: (-23.6861°, -46.6228°)",
      "  Itabaiana: (-10.6850°, -37.4253°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3492.83 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 55098.38 km²",
      "FINAL ANSWER: Area: 55098.38 km², Perimeter: 3492.83 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -41.33333,
        "lon": 173.18333,
        "name": "Richmond"
      },
      {
        "lat": -39.06667,
        "lon": 174.08333,
        "name": "New Plymouth"
      },
      {
        "lat": -36.84103,
        "lon": 174.65223,
        "name": "Te Atatu Peninsula"
      },
      {
        "lat": -39.4926,
        "lon": 176.91233,
        "name": "Napier"
      },
      {
        "lat": -41.13333,
        "lon": 174.85,
        "name": "Porirua"
      }
    ],
    "ground_truth": {
      "area_km2": 80162.08,
      "perimeter_km": 1264.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Richmond: (-41.3333°, 173.1833°)",
      "  New Plymouth: (-39.0667°, 174.0833°)",
      "  Te Atatu Peninsula: (-36.8410°, 174.6522°)",
      "  Napier: (-39.4926°, 176.9123°)",
      "  Porirua: (-41.1333°, 174.8500°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1264.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 80162.08 km²",
      "FINAL ANSWER: Area: 80162.08 km², Perimeter: 1264.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -35.02692,
        "lon": 117.88369,
        "name": "Albany"
      },
      {
        "lat": -33.2792,
        "lon": 115.71504,
        "name": "Australind"
      },
      {
        "lat": -32.5269,
        "lon": 115.7217,
        "name": "Mandurah"
      },
      {
        "lat": -31.89578,
        "lon": 115.76431,
        "name": "Scarborough"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      }
    ],
    "ground_truth": {
      "area_km2": 324848.49,
      "perimeter_km": 4457.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Albany: (-35.0269°, 117.8837°)",
      "  Australind: (-33.2792°, 115.7150°)",
      "  Mandurah: (-32.5269°, 115.7217°)",
      "  Scarborough: (-31.8958°, 115.7643°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4457.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 324848.49 km²",
      "FINAL ANSWER: Area: 324848.49 km², Perimeter: 4457.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.87709,
        "lon": 145.12939,
        "name": "Mount Waverley"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -33.85,
        "lon": 151.03333,
        "name": "Auburn"
      }
    ],
    "ground_truth": {
      "area_km2": 43500.13,
      "perimeter_km": 1476.36,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mount Waverley: (-37.8771°, 145.1294°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Auburn: (-33.8500°, 151.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1476.36 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 43500.13 km²",
      "FINAL ANSWER: Area: 43500.13 km², Perimeter: 1476.36 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.05529,
        "lon": -117.75228,
        "name": "Pomona"
      },
      {
        "lat": 34.26945,
        "lon": -118.78148,
        "name": "Simi Valley"
      },
      {
        "lat": 44.98595,
        "lon": -122.98287,
        "name": "Hayesville"
      },
      {
        "lat": 47.78815,
        "lon": -122.30874,
        "name": "Mountlake Terrace"
      },
      {
        "lat": 32.95373,
        "lon": -96.89028,
        "name": "Carrollton"
      },
      {
        "lat": 32.75957,
        "lon": -97.45835,
        "name": "White Settlement"
      }
    ],
    "ground_truth": {
      "area_km2": 1710297.36,
      "perimeter_km": 6292.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pomona: (34.0553°, -117.7523°)",
      "  Simi Valley: (34.2694°, -118.7815°)",
      "  Hayesville: (44.9860°, -122.9829°)",
      "  Mountlake Terrace: (47.7882°, -122.3087°)",
      "  Carrollton: (32.9537°, -96.8903°)",
      "  White Settlement: (32.7596°, -97.4583°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6292.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1710297.36 km²",
      "FINAL ANSWER: Area: 1710297.36 km², Perimeter: 6292.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 16.07,
        "lon": 120.4025,
        "name": "Mangaldan"
      },
      {
        "lat": 14.2973,
        "lon": 121.4598,
        "name": "Lumbang"
      },
      {
        "lat": 6.89814,
        "lon": 126.00961,
        "name": "Lupon"
      },
      {
        "lat": 7.73028,
        "lon": 125.09889,
        "name": "Quezon"
      }
    ],
    "ground_truth": {
      "area_km2": 27076.54,
      "perimeter_km": 2383.71,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Mangaldan: (16.0700°, 120.4025°)",
      "  Lumbang: (14.2973°, 121.4598°)",
      "  Lupon: (6.8981°, 126.0096°)",
      "  Quezon: (7.7303°, 125.0989°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2383.71 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 27076.54 km²",
      "FINAL ANSWER: Area: 27076.54 km², Perimeter: 2383.71 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -37.73333,
        "lon": 145.15,
        "name": "Eltham"
      },
      {
        "lat": -37.8318,
        "lon": 140.77919,
        "name": "Mount Gambier"
      },
      {
        "lat": -27.49325,
        "lon": 153.05826,
        "name": "Coorparoo"
      }
    ],
    "ground_truth": {
      "area_km2": 206040.72,
      "perimeter_km": 3364.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Eltham: (-37.7333°, 145.1500°)",
      "  Mount Gambier: (-37.8318°, 140.7792°)",
      "  Coorparoo: (-27.4932°, 153.0583°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3364.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 206040.72 km²",
      "FINAL ANSWER: Area: 206040.72 km², Perimeter: 3364.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 25.98454,
        "lon": -80.19894,
        "name": "West Park"
      },
      {
        "lat": 41.4156,
        "lon": -81.92347,
        "name": "North Olmsted"
      },
      {
        "lat": 46.05007,
        "lon": -71.96579,
        "name": "Victoriaville"
      }
    ],
    "ground_truth": {
      "area_km2": 716064.43,
      "perimeter_km": 5021.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  West Park: (25.9845°, -80.1989°)",
      "  North Olmsted: (41.4156°, -81.9235°)",
      "  Victoriaville: (46.0501°, -71.9658°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5021.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 716064.43 km²",
      "FINAL ANSWER: Area: 716064.43 km², Perimeter: 5021.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 13.2954,
        "lon": 19.6966,
        "name": "Umm Hājar"
      },
      {
        "lat": 2.46335,
        "lon": 31.49832,
        "name": "Pakwach"
      },
      {
        "lat": -3.28333,
        "lon": 32.85,
        "name": "Mhango"
      },
      {
        "lat": -8.3,
        "lon": 31.51667,
        "name": "Matai"
      },
      {
        "lat": -1.8628,
        "lon": 29.62541,
        "name": "Ngororero"
      }
    ],
    "ground_truth": {
      "area_km2": 1087862.78,
      "perimeter_km": 5759.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Umm Hājar: (13.2954°, 19.6966°)",
      "  Pakwach: (2.4634°, 31.4983°)",
      "  Mhango: (-3.2833°, 32.8500°)",
      "  Matai: (-8.3000°, 31.5167°)",
      "  Ngororero: (-1.8628°, 29.6254°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5759.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1087862.78 km²",
      "FINAL ANSWER: Area: 1087862.78 km², Perimeter: 5759.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 16.25624,
        "lon": 97.7246,
        "name": "Mudon"
      },
      {
        "lat": 31.16611,
        "lon": 112.58306,
        "name": "Zhongxiang"
      },
      {
        "lat": 36.22107,
        "lon": 118.69663,
        "name": "Yishan"
      },
      {
        "lat": 23.73333,
        "lon": 114.68333,
        "name": "Heyuan"
      },
      {
        "lat": 14.96806,
        "lon": 120.95472,
        "name": "Pantubig"
      }
    ],
    "ground_truth": {
      "area_km2": 2325345.79,
      "perimeter_km": 8143.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Mudon: (16.2562°, 97.7246°)",
      "  Zhongxiang: (31.1661°, 112.5831°)",
      "  Yishan: (36.2211°, 118.6966°)",
      "  Heyuan: (23.7333°, 114.6833°)",
      "  Pantubig: (14.9681°, 120.9547°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 8143.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2325345.79 km²",
      "FINAL ANSWER: Area: 2325345.79 km², Perimeter: 8143.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 51.28635,
        "lon": 7.29388,
        "name": "Schwelm"
      },
      {
        "lat": 52.57601,
        "lon": 13.29389,
        "name": "Tegel"
      },
      {
        "lat": 55.01457,
        "lon": 36.47185,
        "name": "Maloyaroslavets"
      }
    ],
    "ground_truth": {
      "area_km2": 14889.3,
      "perimeter_km": 3948.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Schwelm: (51.2863°, 7.2939°)",
      "  Tegel: (52.5760°, 13.2939°)",
      "  Maloyaroslavets: (55.0146°, 36.4719°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3948.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 14889.30 km²",
      "FINAL ANSWER: Area: 14889.30 km², Perimeter: 3948.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 38.06147,
        "lon": -1.04877,
        "name": "Santomera"
      },
      {
        "lat": 42.64725,
        "lon": -8.88459,
        "name": "Boiro"
      },
      {
        "lat": 53.57077,
        "lon": -1.18454,
        "name": "Adwick le Street"
      },
      {
        "lat": 49.34615,
        "lon": 7.25527,
        "name": "Bexbach"
      },
      {
        "lat": 48.2019,
        "lon": 16.38792,
        "name": "Landstraße"
      },
      {
        "lat": 44.16259,
        "lon": 4.61974,
        "name": "Bagnols-sur-Cèze"
      }
    ],
    "ground_truth": {
      "area_km2": 1683739.72,
      "perimeter_km": 5444.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Santomera: (38.0615°, -1.0488°)",
      "  Boiro: (42.6472°, -8.8846°)",
      "  Adwick le Street: (53.5708°, -1.1845°)",
      "  Bexbach: (49.3462°, 7.2553°)",
      "  Landstraße: (48.2019°, 16.3879°)",
      "  Bagnols-sur-Cèze: (44.1626°, 4.6197°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5444.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1683739.72 km²",
      "FINAL ANSWER: Area: 1683739.72 km², Perimeter: 5444.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 6.67342,
        "lon": -3.96938,
        "name": "Arrah"
      },
      {
        "lat": 10.28333,
        "lon": -4.91667,
        "name": "Niangoloko"
      },
      {
        "lat": 12.87695,
        "lon": 10.45536,
        "name": "Nguru"
      },
      {
        "lat": 9.87342,
        "lon": 7.95407,
        "name": "Kachia"
      },
      {
        "lat": 7.25256,
        "lon": 5.19312,
        "name": "Akure"
      }
    ],
    "ground_truth": {
      "area_km2": 670685.25,
      "perimeter_km": 3978.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Arrah: (6.6734°, -3.9694°)",
      "  Niangoloko: (10.2833°, -4.9167°)",
      "  Nguru: (12.8770°, 10.4554°)",
      "  Kachia: (9.8734°, 7.9541°)",
      "  Akure: (7.2526°, 5.1931°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3978.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 670685.25 km²",
      "FINAL ANSWER: Area: 670685.25 km², Perimeter: 3978.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 24.69285,
        "lon": 108.08376,
        "name": "Hechi"
      },
      {
        "lat": 30.01651,
        "lon": 105.7973,
        "name": "Tangba"
      },
      {
        "lat": 30.08333,
        "lon": 114.95,
        "name": "Daye"
      },
      {
        "lat": 28.8547,
        "lon": 120.73168,
        "name": "Xianju"
      },
      {
        "lat": 22.99376,
        "lon": 114.71311,
        "name": "Pingshan"
      }
    ],
    "ground_truth": {
      "area_km2": 755014.43,
      "perimeter_km": 3677.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hechi: (24.6928°, 108.0838°)",
      "  Tangba: (30.0165°, 105.7973°)",
      "  Daye: (30.0833°, 114.9500°)",
      "  Xianju: (28.8547°, 120.7317°)",
      "  Pingshan: (22.9938°, 114.7131°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3677.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 755014.43 km²",
      "FINAL ANSWER: Area: 755014.43 km², Perimeter: 3677.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 50.77926,
        "lon": 4.24355,
        "name": "Sint-Pieters-Leeuw"
      },
      {
        "lat": 50.54581,
        "lon": -3.49671,
        "name": "Teignmouth"
      },
      {
        "lat": 51.52279,
        "lon": -0.71986,
        "name": "Maidenhead"
      },
      {
        "lat": 53.63301,
        "lon": 9.83945,
        "name": "Halstenbek"
      },
      {
        "lat": 50.90383,
        "lon": 7.40306,
        "name": "Much"
      },
      {
        "lat": 47.6895,
        "lon": 9.83247,
        "name": "Wangen"
      }
    ],
    "ground_truth": {
      "area_km2": 173111.91,
      "perimeter_km": 2794.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sint-Pieters-Leeuw: (50.7793°, 4.2435°)",
      "  Teignmouth: (50.5458°, -3.4967°)",
      "  Maidenhead: (51.5228°, -0.7199°)",
      "  Halstenbek: (53.6330°, 9.8394°)",
      "  Much: (50.9038°, 7.4031°)",
      "  Wangen: (47.6895°, 9.8325°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2794.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 173111.91 km²",
      "FINAL ANSWER: Area: 173111.91 km², Perimeter: 2794.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -23.55083,
        "lon": -51.46083,
        "name": "Apucarana"
      },
      {
        "lat": -12.54528,
        "lon": -55.71139,
        "name": "Sorriso"
      },
      {
        "lat": -15.47949,
        "lon": -44.3652,
        "name": "Januária"
      },
      {
        "lat": -19.31111,
        "lon": -46.04889,
        "name": "São Gotardo"
      },
      {
        "lat": -20.99139,
        "lon": -47.65861,
        "name": "Brodowski"
      }
    ],
    "ground_truth": {
      "area_km2": 755889.04,
      "perimeter_km": 3766.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Apucarana: (-23.5508°, -51.4608°)",
      "  Sorriso: (-12.5453°, -55.7114°)",
      "  Januária: (-15.4795°, -44.3652°)",
      "  São Gotardo: (-19.3111°, -46.0489°)",
      "  Brodowski: (-20.9914°, -47.6586°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3766.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 755889.04 km²",
      "FINAL ANSWER: Area: 755889.04 km², Perimeter: 3766.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.61915,
        "lon": -0.87799,
        "name": "La Unión"
      },
      {
        "lat": 49.46307,
        "lon": 1.09364,
        "name": "Mont-Saint-Aignan"
      },
      {
        "lat": 51.61379,
        "lon": 7.19738,
        "name": "Recklinghausen"
      },
      {
        "lat": 54.23575,
        "lon": 10.27934,
        "name": "Preetz"
      },
      {
        "lat": 49.94782,
        "lon": 11.57893,
        "name": "Bayreuth"
      },
      {
        "lat": 41.99771,
        "lon": 12.61814,
        "name": "Tor Lupara"
      }
    ],
    "ground_truth": {
      "area_km2": 1165381.42,
      "perimeter_km": 4798.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  La Unión: (37.6191°, -0.8780°)",
      "  Mont-Saint-Aignan: (49.4631°, 1.0936°)",
      "  Recklinghausen: (51.6138°, 7.1974°)",
      "  Preetz: (54.2358°, 10.2793°)",
      "  Bayreuth: (49.9478°, 11.5789°)",
      "  Tor Lupara: (41.9977°, 12.6181°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4798.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1165381.42 km²",
      "FINAL ANSWER: Area: 1165381.42 km², Perimeter: 4798.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 41.42861,
        "lon": 2.1741,
        "name": "Vilapicina i la Torre Llobeta"
      },
      {
        "lat": 42.81483,
        "lon": -1.64898,
        "name": "Primer Ensanche"
      },
      {
        "lat": 48.77935,
        "lon": 2.33729,
        "name": "L'Haÿ-les-Roses"
      },
      {
        "lat": 51.7575,
        "lon": 4.16528,
        "name": "Middelharnis"
      },
      {
        "lat": 51.71905,
        "lon": 8.75439,
        "name": "Paderborn"
      }
    ],
    "ground_truth": {
      "area_km2": 359027.83,
      "perimeter_km": 3002.7,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Vilapicina i la Torre Llobeta: (41.4286°, 2.1741°)",
      "  Primer Ensanche: (42.8148°, -1.6490°)",
      "  L'Haÿ-les-Roses: (48.7794°, 2.3373°)",
      "  Middelharnis: (51.7575°, 4.1653°)",
      "  Paderborn: (51.7191°, 8.7544°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3002.70 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 359027.83 km²",
      "FINAL ANSWER: Area: 359027.83 km², Perimeter: 3002.70 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.73564,
        "lon": 105.32632,
        "name": "Gangu Chengguanzhen"
      },
      {
        "lat": 44.67024,
        "lon": 102.17491,
        "name": "Bogd"
      },
      {
        "lat": 33.25333,
        "lon": 126.56181,
        "name": "Seogwipo"
      },
      {
        "lat": 22.36718,
        "lon": 114.12347,
        "name": "Tai Wo Hau"
      },
      {
        "lat": 23.17233,
        "lon": 112.28298,
        "name": "Lubu"
      }
    ],
    "ground_truth": {
      "area_km2": 2538190.62,
      "perimeter_km": 6962.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Gangu Chengguanzhen: (34.7356°, 105.3263°)",
      "  Bogd: (44.6702°, 102.1749°)",
      "  Seogwipo: (33.2533°, 126.5618°)",
      "  Tai Wo Hau: (22.3672°, 114.1235°)",
      "  Lubu: (23.1723°, 112.2830°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6962.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2538190.62 km²",
      "FINAL ANSWER: Area: 2538190.62 km², Perimeter: 6962.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.22661,
        "lon": -121.97468,
        "name": "Los Gatos"
      },
      {
        "lat": 47.78815,
        "lon": -122.30874,
        "name": "Mountlake Terrace"
      },
      {
        "lat": 37.67748,
        "lon": -113.06189,
        "name": "Cedar City"
      },
      {
        "lat": 33.46697,
        "lon": -117.69811,
        "name": "Dana Point"
      }
    ],
    "ground_truth": {
      "area_km2": 640325.18,
      "perimeter_km": 3725.39,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Los Gatos: (37.2266°, -121.9747°)",
      "  Mountlake Terrace: (47.7882°, -122.3087°)",
      "  Cedar City: (37.6775°, -113.0619°)",
      "  Dana Point: (33.4670°, -117.6981°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3725.39 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 640325.18 km²",
      "FINAL ANSWER: Area: 640325.18 km², Perimeter: 3725.39 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.68473,
        "lon": -6.00344,
        "name": "Souk El Arbaa"
      },
      {
        "lat": 35.07465,
        "lon": -1.22431,
        "name": "Bensekrane"
      },
      {
        "lat": 35.65903,
        "lon": -0.52168,
        "name": "Sidi ech Chahmi"
      },
      {
        "lat": 36.4,
        "lon": 10.61667,
        "name": "Hammamet"
      },
      {
        "lat": 31.09755,
        "lon": 31.30312,
        "name": "Nabarūh"
      }
    ],
    "ground_truth": {
      "area_km2": 388965.52,
      "perimeter_km": 7016.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Souk El Arbaa: (34.6847°, -6.0034°)",
      "  Bensekrane: (35.0746°, -1.2243°)",
      "  Sidi ech Chahmi: (35.6590°, -0.5217°)",
      "  Hammamet: (36.4000°, 10.6167°)",
      "  Nabarūh: (31.0975°, 31.3031°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7016.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 388965.52 km²",
      "FINAL ANSWER: Area: 388965.52 km², Perimeter: 7016.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 53.59245,
        "lon": -2.21941,
        "name": "Heywood"
      },
      {
        "lat": 53.56321,
        "lon": 9.94257,
        "name": "Altona-Nord"
      },
      {
        "lat": 45.76873,
        "lon": 4.95883,
        "name": "Décines-Charpieu"
      }
    ],
    "ground_truth": {
      "area_km2": 355362.27,
      "perimeter_km": 2749.93,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Heywood: (53.5924°, -2.2194°)",
      "  Altona-Nord: (53.5632°, 9.9426°)",
      "  Décines-Charpieu: (45.7687°, 4.9588°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2749.93 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 355362.27 km²",
      "FINAL ANSWER: Area: 355362.27 km², Perimeter: 2749.93 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 50.13423,
        "lon": 8.91418,
        "name": "Hanau am Main"
      },
      {
        "lat": 50.55162,
        "lon": 9.67518,
        "name": "Fulda"
      },
      {
        "lat": 45.83111,
        "lon": 16.11639,
        "name": "Sesvete"
      }
    ],
    "ground_truth": {
      "area_km2": 25198.41,
      "perimeter_km": 1498.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hanau am Main: (50.1342°, 8.9142°)",
      "  Fulda: (50.5516°, 9.6752°)",
      "  Sesvete: (45.8311°, 16.1164°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1498.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 25198.41 km²",
      "FINAL ANSWER: Area: 25198.41 km², Perimeter: 1498.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -15.77972,
        "lon": -47.92972,
        "name": "Brasília"
      },
      {
        "lat": -11.86417,
        "lon": -55.5025,
        "name": "Sinop"
      },
      {
        "lat": -11.51917,
        "lon": -37.51167,
        "name": "Indiaroba"
      },
      {
        "lat": -13.4425,
        "lon": -42.23889,
        "name": "Paramirim"
      }
    ],
    "ground_truth": {
      "area_km2": 433452.52,
      "perimeter_km": 4106.29,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Brasília: (-15.7797°, -47.9297°)",
      "  Sinop: (-11.8642°, -55.5025°)",
      "  Indiaroba: (-11.5192°, -37.5117°)",
      "  Paramirim: (-13.4425°, -42.2389°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4106.29 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 433452.52 km²",
      "FINAL ANSWER: Area: 433452.52 km², Perimeter: 4106.29 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 30.52297,
        "lon": -87.90333,
        "name": "Fairhope"
      },
      {
        "lat": 35.75647,
        "lon": -83.97046,
        "name": "Maryville"
      },
      {
        "lat": 43.04812,
        "lon": -76.14742,
        "name": "Syracuse"
      },
      {
        "lat": 40.08927,
        "lon": -75.39602,
        "name": "King of Prussia"
      },
      {
        "lat": 22.49502,
        "lon": -79.54548,
        "name": "Remedios"
      }
    ],
    "ground_truth": {
      "area_km2": 1208249.87,
      "perimeter_km": 5288.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Fairhope: (30.5230°, -87.9033°)",
      "  Maryville: (35.7565°, -83.9705°)",
      "  Syracuse: (43.0481°, -76.1474°)",
      "  King of Prussia: (40.0893°, -75.3960°)",
      "  Remedios: (22.4950°, -79.5455°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5288.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1208249.87 km²",
      "FINAL ANSWER: Area: 1208249.87 km², Perimeter: 5288.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 34.92915,
        "lon": 43.48878,
        "name": "Bayjī"
      },
      {
        "lat": 37.45517,
        "lon": 35.81573,
        "name": "Kozan"
      },
      {
        "lat": 36.90124,
        "lon": 54.07195,
        "name": "Bandar-e Torkaman"
      },
      {
        "lat": 32.59702,
        "lon": 74.14652,
        "name": "Sook Kalan"
      }
    ],
    "ground_truth": {
      "area_km2": 536981.48,
      "perimeter_km": 7085.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Bayjī: (34.9291°, 43.4888°)",
      "  Kozan: (37.4552°, 35.8157°)",
      "  Bandar-e Torkaman: (36.9012°, 54.0720°)",
      "  Sook Kalan: (32.5970°, 74.1465°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7085.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 536981.48 km²",
      "FINAL ANSWER: Area: 536981.48 km², Perimeter: 7085.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.40881,
        "lon": -4.48522,
        "name": "Lucena"
      },
      {
        "lat": 42.82562,
        "lon": -1.61671,
        "name": "Burlata"
      },
      {
        "lat": 54.95,
        "lon": -7.73333,
        "name": "Letterkenny"
      },
      {
        "lat": 51.12637,
        "lon": 15.91979,
        "name": "Złotoryja"
      },
      {
        "lat": 48.89452,
        "lon": 18.04436,
        "name": "Trenčín"
      },
      {
        "lat": 36.9084,
        "lon": 15.13937,
        "name": "Avola"
      }
    ],
    "ground_truth": {
      "area_km2": 3373023.77,
      "perimeter_km": 7078.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Lucena: (37.4088°, -4.4852°)",
      "  Burlata: (42.8256°, -1.6167°)",
      "  Letterkenny: (54.9500°, -7.7333°)",
      "  Złotoryja: (51.1264°, 15.9198°)",
      "  Trenčín: (48.8945°, 18.0444°)",
      "  Avola: (36.9084°, 15.1394°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7078.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 3373023.77 km²",
      "FINAL ANSWER: Area: 3373023.77 km², Perimeter: 7078.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 42.78752,
        "lon": -86.10893,
        "name": "Holland"
      },
      {
        "lat": 42.95947,
        "lon": -85.48975,
        "name": "Forest Hills"
      },
      {
        "lat": 40.58867,
        "lon": -83.12852,
        "name": "Marion"
      },
      {
        "lat": 27.71809,
        "lon": -82.35176,
        "name": "Sun City Center"
      }
    ],
    "ground_truth": {
      "area_km2": 174019.77,
      "perimeter_km": 3524.75,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Holland: (42.7875°, -86.1089°)",
      "  Forest Hills: (42.9595°, -85.4898°)",
      "  Marion: (40.5887°, -83.1285°)",
      "  Sun City Center: (27.7181°, -82.3518°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3524.75 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 174019.77 km²",
      "FINAL ANSWER: Area: 174019.77 km², Perimeter: 3524.75 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -19.05294,
        "lon": -169.91957,
        "name": "Alofi"
      },
      {
        "lat": -13.83333,
        "lon": -171.76666,
        "name": "Apia"
      },
      {
        "lat": -13.28163,
        "lon": -176.17453,
        "name": "Mata-Utu"
      },
      {
        "lat": -18.11094,
        "lon": 178.40943,
        "name": "Lami"
      },
      {
        "lat": -18.14307,
        "lon": 177.50691,
        "name": "Sigatoka"
      },
      {
        "lat": -29.05459,
        "lon": 167.96628,
        "name": "Kingston"
      }
    ],
    "ground_truth": {
      "area_km2": 1411739.62,
      "perimeter_km": 6031.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Alofi: (-19.0529°, -169.9196°)",
      "  Apia: (-13.8333°, -171.7667°)",
      "  Mata-Utu: (-13.2816°, -176.1745°)",
      "  Lami: (-18.1109°, 178.4094°)",
      "  Sigatoka: (-18.1431°, 177.5069°)",
      "  Kingston: (-29.0546°, 167.9663°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6031.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1411739.62 km²",
      "FINAL ANSWER: Area: 1411739.62 km², Perimeter: 6031.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 25.85587,
        "lon": 88.35943,
        "name": "Pīrgaaj"
      },
      {
        "lat": 32.44201,
        "lon": 105.823,
        "name": "Guangyuan"
      },
      {
        "lat": 14.5832,
        "lon": 121.0409,
        "name": "Mandaluyong City"
      },
      {
        "lat": 21.05,
        "lon": 105.8,
        "name": "Nghĩa Đô"
      }
    ],
    "ground_truth": {
      "area_km2": 2252179.61,
      "perimeter_km": 7978.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pīrgaaj: (25.8559°, 88.3594°)",
      "  Guangyuan: (32.4420°, 105.8230°)",
      "  Mandaluyong City: (14.5832°, 121.0409°)",
      "  Nghĩa Đô: (21.0500°, 105.8000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7978.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2252179.61 km²",
      "FINAL ANSWER: Area: 2252179.61 km², Perimeter: 7978.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 31.86541,
        "lon": 73.50875,
        "name": "Sukheke Mandi"
      },
      {
        "lat": 41.25832,
        "lon": 67.96991,
        "name": "Shardara"
      },
      {
        "lat": 27.14872,
        "lon": 79.50078,
        "name": "Chhibrāmau"
      }
    ],
    "ground_truth": {
      "area_km2": 197182.1,
      "perimeter_km": 3826.35,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Sukheke Mandi: (31.8654°, 73.5088°)",
      "  Shardara: (41.2583°, 67.9699°)",
      "  Chhibrāmau: (27.1487°, 79.5008°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3826.35 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 197182.10 km²",
      "FINAL ANSWER: Area: 197182.10 km², Perimeter: 3826.35 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.70988,
        "lon": 144.75483,
        "name": "Taylors Hill"
      },
      {
        "lat": -37.56622,
        "lon": 143.84957,
        "name": "Ballarat"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -32.83211,
        "lon": 151.35623,
        "name": "Cessnock"
      },
      {
        "lat": -33.79176,
        "lon": 151.08057,
        "name": "Eastwood"
      }
    ],
    "ground_truth": {
      "area_km2": 72978.34,
      "perimeter_km": 1780.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Taylors Hill: (-37.7099°, 144.7548°)",
      "  Ballarat: (-37.5662°, 143.8496°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Cessnock: (-32.8321°, 151.3562°)",
      "  Eastwood: (-33.7918°, 151.0806°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 1780.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 72978.34 km²",
      "FINAL ANSWER: Area: 72978.34 km², Perimeter: 1780.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -23.56786,
        "lon": -46.54599,
        "name": "Vila Formosa"
      },
      {
        "lat": -13.65145,
        "lon": -41.84564,
        "name": "Livramento do Brumado"
      },
      {
        "lat": -12.13556,
        "lon": -38.41917,
        "name": "Alagoinhas"
      }
    ],
    "ground_truth": {
      "area_km2": 167429.29,
      "perimeter_km": 3150.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Vila Formosa: (-23.5679°, -46.5460°)",
      "  Livramento do Brumado: (-13.6515°, -41.8456°)",
      "  Alagoinhas: (-12.1356°, -38.4192°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3150.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 167429.29 km²",
      "FINAL ANSWER: Area: 167429.29 km², Perimeter: 3150.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 34.60593,
        "lon": -86.98334,
        "name": "Decatur"
      },
      {
        "lat": 35.61507,
        "lon": -87.03528,
        "name": "Columbia"
      },
      {
        "lat": 42.00864,
        "lon": -87.66672,
        "name": "Rogers Park"
      },
      {
        "lat": 40.3634,
        "lon": -79.86644,
        "name": "West Mifflin"
      },
      {
        "lat": 40.72316,
        "lon": -73.91264,
        "name": "Maspeth"
      },
      {
        "lat": 40.72982,
        "lon": -73.21039,
        "name": "Islip"
      }
    ],
    "ground_truth": {
      "area_km2": 421671.93,
      "perimeter_km": 3454.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Decatur: (34.6059°, -86.9833°)",
      "  Columbia: (35.6151°, -87.0353°)",
      "  Rogers Park: (42.0086°, -87.6667°)",
      "  West Mifflin: (40.3634°, -79.8664°)",
      "  Maspeth: (40.7232°, -73.9126°)",
      "  Islip: (40.7298°, -73.2104°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3454.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 421671.93 km²",
      "FINAL ANSWER: Area: 421671.93 km², Perimeter: 3454.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -7.41667,
        "lon": 30.6,
        "name": "Kirando"
      },
      {
        "lat": -1.9275,
        "lon": 18.2881,
        "name": "Inongo"
      },
      {
        "lat": 14.10776,
        "lon": 34.09197,
        "name": "Al-Fāw"
      },
      {
        "lat": 14.88722,
        "lon": 38.81528,
        "name": "Mendefera"
      },
      {
        "lat": 0.64996,
        "lon": 33.17128,
        "name": "Buwenge"
      },
      {
        "lat": 0.43333,
        "lon": 31.23333,
        "name": "Kasambya"
      }
    ],
    "ground_truth": {
      "area_km2": 2515674.62,
      "perimeter_km": 7295.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Kirando: (-7.4167°, 30.6000°)",
      "  Inongo: (-1.9275°, 18.2881°)",
      "  Al-Fāw: (14.1078°, 34.0920°)",
      "  Mendefera: (14.8872°, 38.8153°)",
      "  Buwenge: (0.6500°, 33.1713°)",
      "  Kasambya: (0.4333°, 31.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7295.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2515674.62 km²",
      "FINAL ANSWER: Area: 2515674.62 km², Perimeter: 7295.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 15.26349,
        "lon": 74.10875,
        "name": "Curchorem"
      },
      {
        "lat": 27.52698,
        "lon": 80.75461,
        "name": "Khairābād"
      },
      {
        "lat": 22.642,
        "lon": 90.42598,
        "name": "Charāmaddi"
      }
    ],
    "ground_truth": {
      "area_km2": 856990.63,
      "perimeter_km": 4541.17,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Curchorem: (15.2635°, 74.1088°)",
      "  Khairābād: (27.5270°, 80.7546°)",
      "  Charāmaddi: (22.6420°, 90.4260°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4541.17 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 856990.63 km²",
      "FINAL ANSWER: Area: 856990.63 km², Perimeter: 4541.17 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -27.20338,
        "lon": 152.95923,
        "name": "Narangba"
      },
      {
        "lat": -27.98941,
        "lon": 153.33633,
        "name": "Nerang"
      }
    ],
    "ground_truth": {
      "area_km2": 12226.39,
      "perimeter_km": 805.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Narangba: (-27.2034°, 152.9592°)",
      "  Nerang: (-27.9894°, 153.3363°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 805.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 12226.39 km²",
      "FINAL ANSWER: Area: 12226.39 km², Perimeter: 805.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -22.27407,
        "lon": 166.44884,
        "name": "Nouméa"
      },
      {
        "lat": -36.88745,
        "lon": 174.77059,
        "name": "Epsom"
      },
      {
        "lat": -44.39672,
        "lon": 171.25364,
        "name": "Timaru"
      }
    ],
    "ground_truth": {
      "area_km2": 595347.33,
      "perimeter_km": 5196.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Nouméa: (-22.2741°, 166.4488°)",
      "  Epsom: (-36.8875°, 174.7706°)",
      "  Timaru: (-44.3967°, 171.2536°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5196.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 595347.33 km²",
      "FINAL ANSWER: Area: 595347.33 km², Perimeter: 5196.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 37.18516,
        "lon": -5.78093,
        "name": "Utrera"
      },
      {
        "lat": 43.66228,
        "lon": -7.59344,
        "name": "Viveiro"
      },
      {
        "lat": 53.56507,
        "lon": -2.12267,
        "name": "Royton"
      },
      {
        "lat": 50.54322,
        "lon": 7.1113,
        "name": "Bad Neuenahr-Ahrweiler"
      },
      {
        "lat": 42.21389,
        "lon": 20.73972,
        "name": "Prizren"
      }
    ],
    "ground_truth": {
      "area_km2": 2133220.45,
      "perimeter_km": 6341.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Utrera: (37.1852°, -5.7809°)",
      "  Viveiro: (43.6623°, -7.5934°)",
      "  Royton: (53.5651°, -2.1227°)",
      "  Bad Neuenahr-Ahrweiler: (50.5432°, 7.1113°)",
      "  Prizren: (42.2139°, 20.7397°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6341.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2133220.45 km²",
      "FINAL ANSWER: Area: 2133220.45 km², Perimeter: 6341.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 9.28358,
        "lon": 76.45519,
        "name": "Haripād"
      },
      {
        "lat": 16.9985,
        "lon": 79.9656,
        "name": "Kodār"
      },
      {
        "lat": 22.06312,
        "lon": 82.13129,
        "name": "Tifrā"
      },
      {
        "lat": 26.97982,
        "lon": 84.85065,
        "name": "Raxaul"
      },
      {
        "lat": 25.10479,
        "lon": 84.1162,
        "name": "Nokha"
      }
    ],
    "ground_truth": {
      "area_km2": 57521.94,
      "perimeter_km": 4315.21,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Haripād: (9.2836°, 76.4552°)",
      "  Kodār: (16.9985°, 79.9656°)",
      "  Tifrā: (22.0631°, 82.1313°)",
      "  Raxaul: (26.9798°, 84.8507°)",
      "  Nokha: (25.1048°, 84.1162°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4315.21 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 57521.94 km²",
      "FINAL ANSWER: Area: 57521.94 km², Perimeter: 4315.21 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -35.28346,
        "lon": 149.12807,
        "name": "Canberra"
      },
      {
        "lat": -37.6,
        "lon": 144.95,
        "name": "Craigieburn"
      },
      {
        "lat": -30.50123,
        "lon": 151.66553,
        "name": "Armidale"
      },
      {
        "lat": -27.94402,
        "lon": 153.39815,
        "name": "Labrador"
      },
      {
        "lat": -30.29626,
        "lon": 153.11351,
        "name": "Coffs Harbour"
      },
      {
        "lat": -33.82346,
        "lon": 150.94607,
        "name": "Greystanes"
      }
    ],
    "ground_truth": {
      "area_km2": 132792.89,
      "perimeter_km": 2724.15,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Canberra: (-35.2835°, 149.1281°)",
      "  Craigieburn: (-37.6000°, 144.9500°)",
      "  Armidale: (-30.5012°, 151.6655°)",
      "  Labrador: (-27.9440°, 153.3981°)",
      "  Coffs Harbour: (-30.2963°, 153.1135°)",
      "  Greystanes: (-33.8235°, 150.9461°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2724.15 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 132792.89 km²",
      "FINAL ANSWER: Area: 132792.89 km², Perimeter: 2724.15 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -19.86528,
        "lon": -47.44,
        "name": "Sacramento"
      },
      {
        "lat": -0.826,
        "lon": -52.506,
        "name": "Laranjal do Jari"
      },
      {
        "lat": -7.03306,
        "lon": -35.85722,
        "name": "Esperança"
      },
      {
        "lat": -16.575,
        "lon": -39.55333,
        "name": "Itabela"
      }
    ],
    "ground_truth": {
      "area_km2": 2126556.12,
      "perimeter_km": 6202.58,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sacramento: (-19.8653°, -47.4400°)",
      "  Laranjal do Jari: (-0.8260°, -52.5060°)",
      "  Esperança: (-7.0331°, -35.8572°)",
      "  Itabela: (-16.5750°, -39.5533°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6202.58 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2126556.12 km²",
      "FINAL ANSWER: Area: 2126556.12 km², Perimeter: 6202.58 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.9,
        "lon": 145.18333,
        "name": "Wheelers Hill"
      },
      {
        "lat": -33.41665,
        "lon": 149.5806,
        "name": "Bathurst"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -33.8188,
        "lon": 151.1062,
        "name": "Ryde"
      }
    ],
    "ground_truth": {
      "area_km2": 131897.47,
      "perimeter_km": 2709.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Wheelers Hill: (-37.9000°, 145.1833°)",
      "  Bathurst: (-33.4166°, 149.5806°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Ryde: (-33.8188°, 151.1062°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2709.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 131897.47 km²",
      "FINAL ANSWER: Area: 131897.47 km², Perimeter: 2709.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 32.46181,
        "lon": -90.11536,
        "name": "Madison"
      },
      {
        "lat": 32.54208,
        "lon": -97.32085,
        "name": "Burleson"
      },
      {
        "lat": 39.83665,
        "lon": -105.0372,
        "name": "Westminster"
      },
      {
        "lat": 42.50309,
        "lon": -83.18354,
        "name": "Berkley"
      },
      {
        "lat": 42.19454,
        "lon": -71.83563,
        "name": "Auburn"
      },
      {
        "lat": 30.36576,
        "lon": -88.55613,
        "name": "Pascagoula"
      }
    ],
    "ground_truth": {
      "area_km2": 2051963.85,
      "perimeter_km": 6785.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Madison: (32.4618°, -90.1154°)",
      "  Burleson: (32.5421°, -97.3208°)",
      "  Westminster: (39.8366°, -105.0372°)",
      "  Berkley: (42.5031°, -83.1835°)",
      "  Auburn: (42.1945°, -71.8356°)",
      "  Pascagoula: (30.3658°, -88.5561°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6785.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2051963.85 km²",
      "FINAL ANSWER: Area: 2051963.85 km², Perimeter: 6785.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 47.30707,
        "lon": 11.06817,
        "name": "Telfs"
      },
      {
        "lat": 52.21667,
        "lon": -0.26667,
        "name": "Saint Neots"
      },
      {
        "lat": 53.0,
        "lon": -1.13333,
        "name": "Arnold"
      },
      {
        "lat": 56.04284,
        "lon": 37.85153,
        "name": "Zavety Il’icha"
      },
      {
        "lat": 53.22186,
        "lon": 26.67679,
        "name": "Nesvizh"
      }
    ],
    "ground_truth": {
      "area_km2": 1158059.26,
      "perimeter_km": 5657.05,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Telfs: (47.3071°, 11.0682°)",
      "  Saint Neots: (52.2167°, -0.2667°)",
      "  Arnold: (53.0000°, -1.1333°)",
      "  Zavety Il’icha: (56.0428°, 37.8515°)",
      "  Nesvizh: (53.2219°, 26.6768°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5657.05 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1158059.26 km²",
      "FINAL ANSWER: Area: 1158059.26 km², Perimeter: 5657.05 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -37.81992,
        "lon": 145.0358,
        "name": "Hawthorn"
      },
      {
        "lat": -38.38176,
        "lon": 142.48799,
        "name": "Warrnambool"
      },
      {
        "lat": -27.62329,
        "lon": 153.04785,
        "name": "Calamvale"
      },
      {
        "lat": -32.73308,
        "lon": 151.5574,
        "name": "Maitland"
      },
      {
        "lat": -33.9049,
        "lon": 151.01996,
        "name": "Yagoona"
      }
    ],
    "ground_truth": {
      "area_km2": 240031.73,
      "perimeter_km": 3196.88,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Hawthorn: (-37.8199°, 145.0358°)",
      "  Warrnambool: (-38.3818°, 142.4880°)",
      "  Calamvale: (-27.6233°, 153.0479°)",
      "  Maitland: (-32.7331°, 151.5574°)",
      "  Yagoona: (-33.9049°, 151.0200°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3196.88 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 240031.73 km²",
      "FINAL ANSWER: Area: 240031.73 km², Perimeter: 3196.88 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 43.27766,
        "lon": 5.43133,
        "name": "Saint-Loup"
      },
      {
        "lat": 50.88637,
        "lon": 7.0583,
        "name": "Porz am Rhein"
      },
      {
        "lat": 52.48419,
        "lon": 13.53185,
        "name": "Karlshorst"
      },
      {
        "lat": 48.20906,
        "lon": 16.37135,
        "name": "Innere Stadt"
      },
      {
        "lat": 40.53123,
        "lon": 17.58522,
        "name": "Francavilla Fontana"
      }
    ],
    "ground_truth": {
      "area_km2": 834492.12,
      "perimeter_km": 3760.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Saint-Loup: (43.2777°, 5.4313°)",
      "  Porz am Rhein: (50.8864°, 7.0583°)",
      "  Karlshorst: (52.4842°, 13.5319°)",
      "  Innere Stadt: (48.2091°, 16.3713°)",
      "  Francavilla Fontana: (40.5312°, 17.5852°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3760.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 834492.12 km²",
      "FINAL ANSWER: Area: 834492.12 km², Perimeter: 3760.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 5.06191,
        "lon": -6.25997,
        "name": "Sahoua"
      },
      {
        "lat": 6.13656,
        "lon": -6.84096,
        "name": "Loboville"
      },
      {
        "lat": 8.56744,
        "lon": -10.1336,
        "name": "Gueckedou"
      },
      {
        "lat": 14.78148,
        "lon": -17.3841,
        "name": "N’diareme limamoulaye"
      },
      {
        "lat": 6.9827,
        "lon": 7.45534,
        "name": "Enugu-Ezike"
      },
      {
        "lat": 5.35444,
        "lon": -4.00167,
        "name": "Abidjan"
      }
    ],
    "ground_truth": {
      "area_km2": 1007828.31,
      "perimeter_km": 6013.42,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sahoua: (5.0619°, -6.2600°)",
      "  Loboville: (6.1366°, -6.8410°)",
      "  Gueckedou: (8.5674°, -10.1336°)",
      "  N’diareme limamoulaye: (14.7815°, -17.3841°)",
      "  Enugu-Ezike: (6.9827°, 7.4553°)",
      "  Abidjan: (5.3544°, -4.0017°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6013.42 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1007828.31 km²",
      "FINAL ANSWER: Area: 1007828.31 km², Perimeter: 6013.42 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.10894,
        "lon": 23.71749,
        "name": "Brest"
      },
      {
        "lat": 52.42719,
        "lon": 22.86231,
        "name": "Siemiatycze"
      },
      {
        "lat": 55.84376,
        "lon": 48.51784,
        "name": "Zelenodolsk"
      }
    ],
    "ground_truth": {
      "area_km2": 47203.07,
      "perimeter_km": 3435.73,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Brest: (52.1089°, 23.7175°)",
      "  Siemiatycze: (52.4272°, 22.8623°)",
      "  Zelenodolsk: (55.8438°, 48.5178°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3435.73 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 47203.07 km²",
      "FINAL ANSWER: Area: 47203.07 km², Perimeter: 3435.73 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -38.08333,
        "lon": 144.38333,
        "name": "Corio"
      },
      {
        "lat": -34.92866,
        "lon": 138.59863,
        "name": "Adelaide"
      },
      {
        "lat": -34.06564,
        "lon": 151.01266,
        "name": "Engadine"
      },
      {
        "lat": -37.81667,
        "lon": 145.23333,
        "name": "Ringwood"
      }
    ],
    "ground_truth": {
      "area_km2": 222012.71,
      "perimeter_km": 2512.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Corio: (-38.0833°, 144.3833°)",
      "  Adelaide: (-34.9287°, 138.5986°)",
      "  Engadine: (-34.0656°, 151.0127°)",
      "  Ringwood: (-37.8167°, 145.2333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2512.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 222012.71 km²",
      "FINAL ANSWER: Area: 222012.71 km², Perimeter: 2512.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 37.5992,
        "lon": -1.31493,
        "name": "Mazarrón"
      },
      {
        "lat": 51.62127,
        "lon": 0.30556,
        "name": "Brentwood"
      },
      {
        "lat": 48.85442,
        "lon": 2.48268,
        "name": "Fontenay-sous-Bois"
      }
    ],
    "ground_truth": {
      "area_km2": 146464.62,
      "perimeter_km": 3197.09,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Mazarrón: (37.5992°, -1.3149°)",
      "  Brentwood: (51.6213°, 0.3056°)",
      "  Fontenay-sous-Bois: (48.8544°, 2.4827°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3197.09 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 146464.62 km²",
      "FINAL ANSWER: Area: 146464.62 km², Perimeter: 3197.09 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 52.30273,
        "lon": -0.69446,
        "name": "Wellingborough"
      },
      {
        "lat": 55.79916,
        "lon": -4.39285,
        "name": "Barrhead"
      },
      {
        "lat": 48.9685,
        "lon": 8.30704,
        "name": "Rheinstetten"
      }
    ],
    "ground_truth": {
      "area_km2": 91548.72,
      "perimeter_km": 2337.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Wellingborough: (52.3027°, -0.6945°)",
      "  Barrhead: (55.7992°, -4.3929°)",
      "  Rheinstetten: (48.9685°, 8.3070°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2337.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 91548.72 km²",
      "FINAL ANSWER: Area: 91548.72 km², Perimeter: 2337.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 27.59178,
        "lon": 68.61848,
        "name": "Pir Jo Goth"
      },
      {
        "lat": 28.86993,
        "lon": 75.9165,
        "name": "Toshām"
      },
      {
        "lat": 40.7046,
        "lon": 72.86666,
        "name": "Kara Suu"
      },
      {
        "lat": 27.47315,
        "lon": 78.3031,
        "name": "Jalesar"
      },
      {
        "lat": 19.77889,
        "lon": 85.17033,
        "name": "Bānapur"
      },
      {
        "lat": 18.42866,
        "lon": 79.86385,
        "name": "Bhupalpally"
      }
    ],
    "ground_truth": {
      "area_km2": 1959617.68,
      "perimeter_km": 6844.43,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Pir Jo Goth: (27.5918°, 68.6185°)",
      "  Toshām: (28.8699°, 75.9165°)",
      "  Kara Suu: (40.7046°, 72.8667°)",
      "  Jalesar: (27.4732°, 78.3031°)",
      "  Bānapur: (19.7789°, 85.1703°)",
      "  Bhupalpally: (18.4287°, 79.8638°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6844.43 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1959617.68 km²",
      "FINAL ANSWER: Area: 1959617.68 km², Perimeter: 6844.43 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 40.42118,
        "lon": -79.7881,
        "name": "Monroeville"
      },
      {
        "lat": 37.77422,
        "lon": -87.11333,
        "name": "Owensboro"
      },
      {
        "lat": 42.24481,
        "lon": -83.06095,
        "name": "LaSalle"
      },
      {
        "lat": 43.65498,
        "lon": -79.37153,
        "name": "Moss Park"
      },
      {
        "lat": 42.81259,
        "lon": -70.87728,
        "name": "Newburyport"
      },
      {
        "lat": 41.39482,
        "lon": -73.45401,
        "name": "Danbury"
      }
    ],
    "ground_truth": {
      "area_km2": 314274.72,
      "perimeter_km": 3142.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Monroeville: (40.4212°, -79.7881°)",
      "  Owensboro: (37.7742°, -87.1133°)",
      "  LaSalle: (42.2448°, -83.0610°)",
      "  Moss Park: (43.6550°, -79.3715°)",
      "  Newburyport: (42.8126°, -70.8773°)",
      "  Danbury: (41.3948°, -73.4540°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3142.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 314274.72 km²",
      "FINAL ANSWER: Area: 314274.72 km², Perimeter: 3142.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.82346,
        "lon": -97.17057,
        "name": "Hurst"
      },
      {
        "lat": 39.95087,
        "lon": -86.26194,
        "name": "Zionsville"
      },
      {
        "lat": 45.46536,
        "lon": -73.66585,
        "name": "Côte-Saint-Luc"
      }
    ],
    "ground_truth": {
      "area_km2": 10007.16,
      "perimeter_km": 4903.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Hurst: (32.8235°, -97.1706°)",
      "  Zionsville: (39.9509°, -86.2619°)",
      "  Côte-Saint-Luc: (45.4654°, -73.6659°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4903.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 10007.16 km²",
      "FINAL ANSWER: Area: 10007.16 km², Perimeter: 4903.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 7.73909,
        "lon": -7.61377,
        "name": "Biankouma"
      },
      {
        "lat": 9.50511,
        "lon": -7.56433,
        "name": "Odienné"
      },
      {
        "lat": 12.70354,
        "lon": -7.96463,
        "name": "Dialakorodji"
      },
      {
        "lat": 5.51737,
        "lon": 5.75006,
        "name": "Warri"
      },
      {
        "lat": 6.38423,
        "lon": -3.88759,
        "name": "Akoupé"
      }
    ],
    "ground_truth": {
      "area_km2": 475546.23,
      "perimeter_km": 3766.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Biankouma: (7.7391°, -7.6138°)",
      "  Odienné: (9.5051°, -7.5643°)",
      "  Dialakorodji: (12.7035°, -7.9646°)",
      "  Warri: (5.5174°, 5.7501°)",
      "  Akoupé: (6.3842°, -3.8876°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3766.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 475546.23 km²",
      "FINAL ANSWER: Area: 475546.23 km², Perimeter: 3766.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.25038,
        "lon": -3.83062,
        "name": "Humanes de Madrid"
      },
      {
        "lat": 53.10434,
        "lon": -2.02207,
        "name": "Leek"
      },
      {
        "lat": 52.25,
        "lon": -0.88333,
        "name": "Northampton"
      },
      {
        "lat": 51.87819,
        "lon": 0.55292,
        "name": "Braintree"
      },
      {
        "lat": 49.05,
        "lon": 2.1,
        "name": "Pontoise"
      }
    ],
    "ground_truth": {
      "area_km2": 264903.53,
      "perimeter_km": 3081.77,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Humanes de Madrid: (40.2504°, -3.8306°)",
      "  Leek: (53.1043°, -2.0221°)",
      "  Northampton: (52.2500°, -0.8833°)",
      "  Braintree: (51.8782°, 0.5529°)",
      "  Pontoise: (49.0500°, 2.1000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3081.77 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 264903.53 km²",
      "FINAL ANSWER: Area: 264903.53 km², Perimeter: 3081.77 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 32.89953,
        "lon": -105.96027,
        "name": "Alamogordo"
      },
      {
        "lat": 43.88441,
        "lon": -91.23514,
        "name": "Onalaska"
      },
      {
        "lat": 41.95781,
        "lon": -87.76506,
        "name": "Portage Park"
      },
      {
        "lat": 37.13179,
        "lon": -80.57645,
        "name": "Radford"
      }
    ],
    "ground_truth": {
      "area_km2": 1012859.06,
      "perimeter_km": 5289.45,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Alamogordo: (32.8995°, -105.9603°)",
      "  Onalaska: (43.8844°, -91.2351°)",
      "  Portage Park: (41.9578°, -87.7651°)",
      "  Radford: (37.1318°, -80.5764°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5289.45 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1012859.06 km²",
      "FINAL ANSWER: Area: 1012859.06 km², Perimeter: 5289.45 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 36.67774,
        "lon": -121.6555,
        "name": "Salinas"
      },
      {
        "lat": 49.16667,
        "lon": -123.13333,
        "name": "Brighouse-City Centre"
      },
      {
        "lat": 49.88307,
        "lon": -119.48568,
        "name": "Kelowna"
      },
      {
        "lat": 34.05168,
        "lon": -117.9684,
        "name": "West Puente Valley"
      }
    ],
    "ground_truth": {
      "area_km2": 461940.66,
      "perimeter_km": 3877.44,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Salinas: (36.6777°, -121.6555°)",
      "  Brighouse-City Centre: (49.1667°, -123.1333°)",
      "  Kelowna: (49.8831°, -119.4857°)",
      "  West Puente Valley: (34.0517°, -117.9684°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3877.44 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 461940.66 km²",
      "FINAL ANSWER: Area: 461940.66 km², Perimeter: 3877.44 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -34.42603,
        "lon": -58.57962,
        "name": "Tigre"
      },
      {
        "lat": -23.31028,
        "lon": -51.16278,
        "name": "Londrina"
      },
      {
        "lat": -22.75361,
        "lon": -47.41361,
        "name": "Santa Bárbara d'Oeste"
      }
    ],
    "ground_truth": {
      "area_km2": 223433.28,
      "perimeter_km": 3511.49,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Tigre: (-34.4260°, -58.5796°)",
      "  Londrina: (-23.3103°, -51.1628°)",
      "  Santa Bárbara d'Oeste: (-22.7536°, -47.4136°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3511.49 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 223433.28 km²",
      "FINAL ANSWER: Area: 223433.28 km², Perimeter: 3511.49 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 50.46198,
        "lon": -3.52522,
        "name": "Torquay"
      },
      {
        "lat": 50.66667,
        "lon": 3.08333,
        "name": "Marcq-en-Barœul"
      },
      {
        "lat": 52.25917,
        "lon": 4.75972,
        "name": "Aalsmeer"
      },
      {
        "lat": 43.8805,
        "lon": 11.09699,
        "name": "Prato"
      }
    ],
    "ground_truth": {
      "area_km2": 351585.22,
      "perimeter_km": 3043.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Torquay: (50.4620°, -3.5252°)",
      "  Marcq-en-Barœul: (50.6667°, 3.0833°)",
      "  Aalsmeer: (52.2592°, 4.7597°)",
      "  Prato: (43.8805°, 11.0970°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3043.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 351585.22 km²",
      "FINAL ANSWER: Area: 351585.22 km², Perimeter: 3043.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -25.44613,
        "lon": -56.43928,
        "name": "Coronel Oviedo"
      },
      {
        "lat": -20.78765,
        "lon": -51.70338,
        "name": "Três Lagoas"
      },
      {
        "lat": -12.67,
        "lon": -39.10194,
        "name": "Cruz das Almas"
      },
      {
        "lat": -22.11667,
        "lon": -43.20917,
        "name": "Três Rios"
      },
      {
        "lat": -23.53936,
        "lon": -46.51788,
        "name": "Vila Matilde"
      },
      {
        "lat": -22.97056,
        "lon": -46.99583,
        "name": "Valinhos"
      }
    ],
    "ground_truth": {
      "area_km2": 836083.18,
      "perimeter_km": 4912.14,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Coronel Oviedo: (-25.4461°, -56.4393°)",
      "  Três Lagoas: (-20.7876°, -51.7034°)",
      "  Cruz das Almas: (-12.6700°, -39.1019°)",
      "  Três Rios: (-22.1167°, -43.2092°)",
      "  Vila Matilde: (-23.5394°, -46.5179°)",
      "  Valinhos: (-22.9706°, -46.9958°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4912.14 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 836083.18 km²",
      "FINAL ANSWER: Area: 836083.18 km², Perimeter: 4912.14 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.25424,
        "lon": -85.75941,
        "name": "Louisville"
      },
      {
        "lat": 40.4284,
        "lon": -79.69755,
        "name": "Murrysville"
      },
      {
        "lat": 40.57927,
        "lon": -74.41154,
        "name": "South Plainfield"
      }
    ],
    "ground_truth": {
      "area_km2": 42072.45,
      "perimeter_km": 2029.33,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Louisville: (38.2542°, -85.7594°)",
      "  Murrysville: (40.4284°, -79.6976°)",
      "  South Plainfield: (40.5793°, -74.4115°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2029.33 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 42072.45 km²",
      "FINAL ANSWER: Area: 42072.45 km², Perimeter: 2029.33 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 38.70712,
        "lon": -121.28106,
        "name": "Citrus Heights"
      },
      {
        "lat": 49.02049,
        "lon": -122.79507,
        "name": "White Rock"
      },
      {
        "lat": 51.03951,
        "lon": -114.07087,
        "name": "Beltline"
      },
      {
        "lat": 33.77974,
        "lon": -116.46529,
        "name": "Cathedral City"
      }
    ],
    "ground_truth": {
      "area_km2": 817970.23,
      "perimeter_km": 4441.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Citrus Heights: (38.7071°, -121.2811°)",
      "  White Rock: (49.0205°, -122.7951°)",
      "  Beltline: (51.0395°, -114.0709°)",
      "  Cathedral City: (33.7797°, -116.4653°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4441.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 817970.23 km²",
      "FINAL ANSWER: Area: 817970.23 km², Perimeter: 4441.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 48.40821,
        "lon": 33.70919,
        "name": "Pyatykhatky"
      },
      {
        "lat": 49.02894,
        "lon": 33.43847,
        "name": "Kriukiv"
      },
      {
        "lat": 59.15838,
        "lon": 57.5705,
        "name": "Aleksandrovsk"
      },
      {
        "lat": 56.44222,
        "lon": 60.18778,
        "name": "Polevskoy"
      }
    ],
    "ground_truth": {
      "area_km2": 395007.51,
      "perimeter_km": 4317.38,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Pyatykhatky: (48.4082°, 33.7092°)",
      "  Kriukiv: (49.0289°, 33.4385°)",
      "  Aleksandrovsk: (59.1584°, 57.5705°)",
      "  Polevskoy: (56.4422°, 60.1878°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4317.38 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 395007.51 km²",
      "FINAL ANSWER: Area: 395007.51 km², Perimeter: 4317.38 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 51.75,
        "lon": -2.2,
        "name": "Stroud"
      },
      {
        "lat": 53.29483,
        "lon": -3.72674,
        "name": "Colwyn Bay"
      },
      {
        "lat": 55.94433,
        "lon": -4.57061,
        "name": "Dumbarton"
      },
      {
        "lat": 41.91886,
        "lon": 8.73812,
        "name": "Ajaccio"
      },
      {
        "lat": 43.31083,
        "lon": 3.47583,
        "name": "Agde"
      }
    ],
    "ground_truth": {
      "area_km2": 329084.4,
      "perimeter_km": 3818.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Stroud: (51.7500°, -2.2000°)",
      "  Colwyn Bay: (53.2948°, -3.7267°)",
      "  Dumbarton: (55.9443°, -4.5706°)",
      "  Ajaccio: (41.9189°, 8.7381°)",
      "  Agde: (43.3108°, 3.4758°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3818.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 329084.40 km²",
      "FINAL ANSWER: Area: 329084.40 km², Perimeter: 3818.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.79833,
        "lon": 117.86639,
        "name": "Guanshan"
      },
      {
        "lat": 35.63333,
        "lon": 134.63333,
        "name": "Kasumi"
      },
      {
        "lat": 35.48333,
        "lon": 136.91667,
        "name": "Sekimachi"
      },
      {
        "lat": 34.92633,
        "lon": 134.84533,
        "name": "Kasai"
      }
    ],
    "ground_truth": {
      "area_km2": 69619.31,
      "perimeter_km": 3511.1,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Guanshan: (33.7983°, 117.8664°)",
      "  Kasumi: (35.6333°, 134.6333°)",
      "  Sekimachi: (35.4833°, 136.9167°)",
      "  Kasai: (34.9263°, 134.8453°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3511.10 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 69619.31 km²",
      "FINAL ANSWER: Area: 69619.31 km², Perimeter: 3511.10 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 19.09457,
        "lon": 74.73843,
        "name": "Ahilyanagar"
      },
      {
        "lat": 21.62878,
        "lon": 69.63386,
        "name": "Chhaya"
      },
      {
        "lat": 24.89843,
        "lon": 88.52844,
        "name": "Mohāmmadpur"
      },
      {
        "lat": 22.88333,
        "lon": 87.78333,
        "name": "Arāmbāgh"
      }
    ],
    "ground_truth": {
      "area_km2": 532099.4,
      "perimeter_km": 4218.55,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Ahilyanagar: (19.0946°, 74.7384°)",
      "  Chhaya: (21.6288°, 69.6339°)",
      "  Mohāmmadpur: (24.8984°, 88.5284°)",
      "  Arāmbāgh: (22.8833°, 87.7833°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4218.55 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 532099.40 km²",
      "FINAL ANSWER: Area: 532099.40 km², Perimeter: 4218.55 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 10.86225,
        "lon": 0.20762,
        "name": "Dapaong"
      },
      {
        "lat": 14.00776,
        "lon": 0.75306,
        "name": "Téra"
      },
      {
        "lat": 5.20131,
        "lon": 7.98373,
        "name": "Itu"
      },
      {
        "lat": 7.49748,
        "lon": 5.23041,
        "name": "Ikere-Ekiti"
      }
    ],
    "ground_truth": {
      "area_km2": 181981.69,
      "perimeter_km": 2677.53,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Dapaong: (10.8622°, 0.2076°)",
      "  Téra: (14.0078°, 0.7531°)",
      "  Itu: (5.2013°, 7.9837°)",
      "  Ikere-Ekiti: (7.4975°, 5.2304°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2677.53 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 181981.69 km²",
      "FINAL ANSWER: Area: 181981.69 km², Perimeter: 2677.53 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.62581,
        "lon": 144.92555,
        "name": "Roxburgh Park"
      },
      {
        "lat": -27.22426,
        "lon": 153.02075,
        "name": "North Lakes"
      },
      {
        "lat": -28.07071,
        "lon": 153.39329,
        "name": "Robina"
      },
      {
        "lat": -33.73333,
        "lon": 150.93284,
        "name": "Glenwood"
      }
    ],
    "ground_truth": {
      "area_km2": 167629.23,
      "perimeter_km": 2849.22,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Roxburgh Park: (-37.6258°, 144.9255°)",
      "  North Lakes: (-27.2243°, 153.0207°)",
      "  Robina: (-28.0707°, 153.3933°)",
      "  Glenwood: (-33.7333°, 150.9328°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2849.22 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 167629.23 km²",
      "FINAL ANSWER: Area: 167629.23 km², Perimeter: 2849.22 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 55.7068,
        "lon": 21.13912,
        "name": "Klaipėda"
      },
      {
        "lat": 66.31278,
        "lon": 14.14278,
        "name": "Mo i Rana"
      },
      {
        "lat": 56.01931,
        "lon": 39.94848,
        "name": "Lakinsk"
      },
      {
        "lat": 55.59525,
        "lon": 37.05235,
        "name": "Krasnoznamensk"
      }
    ],
    "ground_truth": {
      "area_km2": 762137.04,
      "perimeter_km": 4192.89,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Klaipėda: (55.7068°, 21.1391°)",
      "  Mo i Rana: (66.3128°, 14.1428°)",
      "  Lakinsk: (56.0193°, 39.9485°)",
      "  Krasnoznamensk: (55.5953°, 37.0523°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4192.89 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 762137.04 km²",
      "FINAL ANSWER: Area: 762137.04 km², Perimeter: 4192.89 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 48.84133,
        "lon": -123.68596,
        "name": "North Cowichan"
      },
      {
        "lat": 47.97898,
        "lon": -122.20208,
        "name": "Everett"
      },
      {
        "lat": 49.15531,
        "lon": -123.15706,
        "name": "Blundell"
      },
      {
        "lat": 47.50024,
        "lon": -111.30081,
        "name": "Great Falls"
      },
      {
        "lat": 34.25223,
        "lon": -118.28841,
        "name": "Tujunga"
      }
    ],
    "ground_truth": {
      "area_km2": 749630.99,
      "perimeter_km": 4455.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  North Cowichan: (48.8413°, -123.6860°)",
      "  Everett: (47.9790°, -122.2021°)",
      "  Blundell: (49.1553°, -123.1571°)",
      "  Great Falls: (47.5002°, -111.3008°)",
      "  Tujunga: (34.2522°, -118.2884°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4455.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 749630.99 km²",
      "FINAL ANSWER: Area: 749630.99 km², Perimeter: 4455.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 49.2818,
        "lon": 9.68352,
        "name": "Künzelsau"
      },
      {
        "lat": 48.21563,
        "lon": 18.60705,
        "name": "Levice"
      },
      {
        "lat": 35.0125,
        "lon": 34.05833,
        "name": "Protaras"
      }
    ],
    "ground_truth": {
      "area_km2": 325842.86,
      "perimeter_km": 5148.56,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Künzelsau: (49.2818°, 9.6835°)",
      "  Levice: (48.2156°, 18.6071°)",
      "  Protaras: (35.0125°, 34.0583°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5148.56 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 325842.86 km²",
      "FINAL ANSWER: Area: 325842.86 km², Perimeter: 5148.56 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 37.3925,
        "lon": 126.92694,
        "name": "Anyang-si"
      },
      {
        "lat": 40.9241,
        "lon": 122.80437,
        "name": "Nantai"
      },
      {
        "lat": 44.02127,
        "lon": 144.26971,
        "name": "Abashiri"
      },
      {
        "lat": 34.68505,
        "lon": 135.80485,
        "name": "Nara-shi"
      }
    ],
    "ground_truth": {
      "area_km2": 966465.76,
      "perimeter_km": 4437.06,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Anyang-si: (37.3925°, 126.9269°)",
      "  Nantai: (40.9241°, 122.8044°)",
      "  Abashiri: (44.0213°, 144.2697°)",
      "  Nara-shi: (34.6850°, 135.8048°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4437.06 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 966465.76 km²",
      "FINAL ANSWER: Area: 966465.76 km², Perimeter: 4437.06 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -36.8582,
        "lon": 174.62019,
        "name": "Lincoln"
      },
      {
        "lat": -37.78333,
        "lon": 175.28333,
        "name": "Hamilton"
      },
      {
        "lat": -40.91667,
        "lon": 175.01667,
        "name": "Paraparaumu"
      }
    ],
    "ground_truth": {
      "area_km2": 11435.67,
      "perimeter_km": 920.16,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Lincoln: (-36.8582°, 174.6202°)",
      "  Hamilton: (-37.7833°, 175.2833°)",
      "  Paraparaumu: (-40.9167°, 175.0167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 920.16 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 11435.67 km²",
      "FINAL ANSWER: Area: 11435.67 km², Perimeter: 920.16 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 41.54211,
        "lon": 2.4445,
        "name": "Mataró"
      },
      {
        "lat": 39.98567,
        "lon": -0.04935,
        "name": "Castelló de la Plana"
      },
      {
        "lat": 38.69875,
        "lon": -9.19289,
        "name": "Belém"
      },
      {
        "lat": 51.23228,
        "lon": -0.3338,
        "name": "Dorking"
      },
      {
        "lat": 45.44694,
        "lon": 8.62118,
        "name": "Novara"
      },
      {
        "lat": 46.71332,
        "lon": 20.14241,
        "name": "Csongrád"
      }
    ],
    "ground_truth": {
      "area_km2": 1065204.39,
      "perimeter_km": 5968.07,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Mataró: (41.5421°, 2.4445°)",
      "  Castelló de la Plana: (39.9857°, -0.0493°)",
      "  Belém: (38.6987°, -9.1929°)",
      "  Dorking: (51.2323°, -0.3338°)",
      "  Novara: (45.4469°, 8.6212°)",
      "  Csongrád: (46.7133°, 20.1424°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5968.07 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1065204.39 km²",
      "FINAL ANSWER: Area: 1065204.39 km², Perimeter: 5968.07 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.70102,
        "lon": -9.17145,
        "name": "Alcântara"
      },
      {
        "lat": 46.34015,
        "lon": 2.60254,
        "name": "Montluçon"
      },
      {
        "lat": 47.42642,
        "lon": 9.65851,
        "name": "Lustenau"
      }
    ],
    "ground_truth": {
      "area_km2": 133041.89,
      "perimeter_km": 3636.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Alcântara: (38.7010°, -9.1715°)",
      "  Montluçon: (46.3402°, 2.6025°)",
      "  Lustenau: (47.4264°, 9.6585°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3636.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 133041.89 km²",
      "FINAL ANSWER: Area: 133041.89 km², Perimeter: 3636.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -29.66917,
        "lon": -52.78889,
        "name": "Candelária"
      },
      {
        "lat": -28.2925,
        "lon": -53.50167,
        "name": "Panambi"
      },
      {
        "lat": -23.15306,
        "lon": -47.05778,
        "name": "Itupeva"
      },
      {
        "lat": -20.10667,
        "lon": -43.04889,
        "name": "Alvinópolis"
      },
      {
        "lat": -23.45947,
        "lon": -46.64086,
        "name": "Mandaqui"
      }
    ],
    "ground_truth": {
      "area_km2": 154559.57,
      "perimeter_km": 3012.76,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Candelária: (-29.6692°, -52.7889°)",
      "  Panambi: (-28.2925°, -53.5017°)",
      "  Itupeva: (-23.1531°, -47.0578°)",
      "  Alvinópolis: (-20.1067°, -43.0489°)",
      "  Mandaqui: (-23.4595°, -46.6409°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3012.76 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 154559.57 km²",
      "FINAL ANSWER: Area: 154559.57 km², Perimeter: 3012.76 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 33.56504,
        "lon": -117.72712,
        "name": "Aliso Viejo"
      },
      {
        "lat": 37.36605,
        "lon": -121.82718,
        "name": "Alum Rock"
      },
      {
        "lat": 46.13817,
        "lon": -122.93817,
        "name": "Longview"
      },
      {
        "lat": 25.18909,
        "lon": -99.82865,
        "name": "Montemorelos"
      }
    ],
    "ground_truth": {
      "area_km2": 1304882.65,
      "perimeter_km": 6611.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Aliso Viejo: (33.5650°, -117.7271°)",
      "  Alum Rock: (37.3661°, -121.8272°)",
      "  Longview: (46.1382°, -122.9382°)",
      "  Montemorelos: (25.1891°, -99.8286°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6611.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1304882.65 km²",
      "FINAL ANSWER: Area: 1304882.65 km², Perimeter: 6611.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 22.56667,
        "lon": 59.52889,
        "name": "Sur"
      },
      {
        "lat": 26.26841,
        "lon": 73.00594,
        "name": "Jodhpur"
      },
      {
        "lat": 29.69197,
        "lon": 76.98448,
        "name": "Karnāl"
      },
      {
        "lat": 16.07786,
        "lon": 75.81321,
        "name": "Kamatgi"
      }
    ],
    "ground_truth": {
      "area_km2": 1522808.94,
      "perimeter_km": 5341.4,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sur: (22.5667°, 59.5289°)",
      "  Jodhpur: (26.2684°, 73.0059°)",
      "  Karnāl: (29.6920°, 76.9845°)",
      "  Kamatgi: (16.0779°, 75.8132°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5341.40 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1522808.94 km²",
      "FINAL ANSWER: Area: 1522808.94 km², Perimeter: 5341.40 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 39.5,
        "lon": -0.35,
        "name": "Alboraya"
      },
      {
        "lat": 54.4858,
        "lon": 9.05239,
        "name": "Husum"
      },
      {
        "lat": 51.31667,
        "lon": 9.5,
        "name": "Kassel"
      }
    ],
    "ground_truth": {
      "area_km2": 169135.55,
      "perimeter_km": 3681.79,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Alboraya: (39.5000°, -0.3500°)",
      "  Husum: (54.4858°, 9.0524°)",
      "  Kassel: (51.3167°, 9.5000°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3681.79 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 169135.55 km²",
      "FINAL ANSWER: Area: 169135.55 km², Perimeter: 3681.79 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": -27.46784,
        "lon": -58.8344,
        "name": "Corrientes"
      },
      {
        "lat": -26.8708,
        "lon": -60.21537,
        "name": "Quitilipi"
      },
      {
        "lat": -9.84139,
        "lon": -39.48167,
        "name": "Uauá"
      },
      {
        "lat": -22.87278,
        "lon": -42.34306,
        "name": "Araruama"
      },
      {
        "lat": -24.6925,
        "lon": -48.00222,
        "name": "Jacupiranga"
      }
    ],
    "ground_truth": {
      "area_km2": 1299322.56,
      "perimeter_km": 6252.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Corrientes: (-27.4678°, -58.8344°)",
      "  Quitilipi: (-26.8708°, -60.2154°)",
      "  Uauá: (-9.8414°, -39.4817°)",
      "  Araruama: (-22.8728°, -42.3431°)",
      "  Jacupiranga: (-24.6925°, -48.0022°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6252.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1299322.56 km²",
      "FINAL ANSWER: Area: 1299322.56 km², Perimeter: 6252.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 8.18122,
        "lon": 9.74431,
        "name": "Ibi"
      },
      {
        "lat": 12.15,
        "lon": 27.35,
        "name": "Ghubaysh"
      },
      {
        "lat": -2.55,
        "lon": 33.03333,
        "name": "Kisesa"
      }
    ],
    "ground_truth": {
      "area_km2": 1734146.39,
      "perimeter_km": 6572.18,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Ibi: (8.1812°, 9.7443°)",
      "  Ghubaysh: (12.1500°, 27.3500°)",
      "  Kisesa: (-2.5500°, 33.0333°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6572.18 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1734146.39 km²",
      "FINAL ANSWER: Area: 1734146.39 km², Perimeter: 6572.18 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 37.07381,
        "lon": 14.24038,
        "name": "Gela"
      },
      {
        "lat": 41.97489,
        "lon": 2.79281,
        "name": "Salt"
      },
      {
        "lat": 43.16296,
        "lon": 13.72274,
        "name": "Fermo"
      },
      {
        "lat": 42.35861,
        "lon": 20.825,
        "name": "Suva Reka"
      },
      {
        "lat": 44.60789,
        "lon": 40.10242,
        "name": "Maykop"
      },
      {
        "lat": 37.96427,
        "lon": 23.49649,
        "name": "Salamína"
      }
    ],
    "ground_truth": {
      "area_km2": 1130551.85,
      "perimeter_km": 6573.37,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Gela: (37.0738°, 14.2404°)",
      "  Salt: (41.9749°, 2.7928°)",
      "  Fermo: (43.1630°, 13.7227°)",
      "  Suva Reka: (42.3586°, 20.8250°)",
      "  Maykop: (44.6079°, 40.1024°)",
      "  Salamína: (37.9643°, 23.4965°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6573.37 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1130551.85 km²",
      "FINAL ANSWER: Area: 1130551.85 km², Perimeter: 6573.37 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 16.85438,
        "lon": 74.56417,
        "name": "Sāngli"
      },
      {
        "lat": 20.81214,
        "lon": 72.99811,
        "name": "Gandevi"
      },
      {
        "lat": 17.45081,
        "lon": 78.68366,
        "name": "Ghatkesar"
      },
      {
        "lat": 10.78974,
        "lon": 76.21898,
        "name": "Ongallur-II"
      }
    ],
    "ground_truth": {
      "area_km2": 255985.25,
      "perimeter_km": 2658.85,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Sāngli: (16.8544°, 74.5642°)",
      "  Gandevi: (20.8121°, 72.9981°)",
      "  Ghatkesar: (17.4508°, 78.6837°)",
      "  Ongallur-II: (10.7897°, 76.2190°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2658.85 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 255985.25 km²",
      "FINAL ANSWER: Area: 255985.25 km², Perimeter: 2658.85 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 13.31536,
        "lon": 12.61135,
        "name": "Diffa"
      },
      {
        "lat": 13.47481,
        "lon": 22.45744,
        "name": "El Geneina Fort"
      },
      {
        "lat": 1.35639,
        "lon": 31.22222,
        "name": "Kikube"
      }
    ],
    "ground_truth": {
      "area_km2": 719667.98,
      "perimeter_km": 5164.46,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Diffa: (13.3154°, 12.6113°)",
      "  El Geneina Fort: (13.4748°, 22.4574°)",
      "  Kikube: (1.3564°, 31.2222°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5164.46 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 719667.98 km²",
      "FINAL ANSWER: Area: 719667.98 km², Perimeter: 5164.46 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -11.60389,
        "lon": -38.58313,
        "name": "Sátiro Dias"
      },
      {
        "lat": -14.06694,
        "lon": -39.64056,
        "name": "Ibirataia"
      },
      {
        "lat": -10.46139,
        "lon": -40.18944,
        "name": "Senhor do Bonfim"
      },
      {
        "lat": -3.60722,
        "lon": -38.96833,
        "name": "São Gonçalo do Amarante"
      },
      {
        "lat": -4.45194,
        "lon": -37.79722,
        "name": "Fortim"
      },
      {
        "lat": -6.96596,
        "lon": -35.7951,
        "name": "Remígio"
      }
    ],
    "ground_truth": {
      "area_km2": 262515.9,
      "perimeter_km": 2592.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Sátiro Dias: (-11.6039°, -38.5831°)",
      "  Ibirataia: (-14.0669°, -39.6406°)",
      "  Senhor do Bonfim: (-10.4614°, -40.1894°)",
      "  São Gonçalo do Amarante: (-3.6072°, -38.9683°)",
      "  Fortim: (-4.4519°, -37.7972°)",
      "  Remígio: (-6.9660°, -35.7951°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2592.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 262515.90 km²",
      "FINAL ANSWER: Area: 262515.90 km², Perimeter: 2592.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -24.50944,
        "lon": -48.8425,
        "name": "Apiaí"
      },
      {
        "lat": -20.33944,
        "lon": -47.78056,
        "name": "Ituverava"
      },
      {
        "lat": -16.3575,
        "lon": -46.90611,
        "name": "Unaí"
      },
      {
        "lat": -15.56833,
        "lon": -40.42306,
        "name": "Macarani"
      },
      {
        "lat": -21.55139,
        "lon": -45.43028,
        "name": "Varginha"
      },
      {
        "lat": -22.55417,
        "lon": -45.78,
        "name": "Paraisópolis"
      }
    ],
    "ground_truth": {
      "area_km2": 348398.95,
      "perimeter_km": 2973.86,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Apiaí: (-24.5094°, -48.8425°)",
      "  Ituverava: (-20.3394°, -47.7806°)",
      "  Unaí: (-16.3575°, -46.9061°)",
      "  Macarani: (-15.5683°, -40.4231°)",
      "  Varginha: (-21.5514°, -45.4303°)",
      "  Paraisópolis: (-22.5542°, -45.7800°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2973.86 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 348398.95 km²",
      "FINAL ANSWER: Area: 348398.95 km², Perimeter: 2973.86 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 42.50779,
        "lon": 1.52109,
        "name": "Andorra la Vella"
      },
      {
        "lat": 36.92077,
        "lon": -6.07529,
        "name": "Lebrija"
      },
      {
        "lat": 53.39234,
        "lon": -2.63994,
        "name": "Great Sankey"
      },
      {
        "lat": 48.69676,
        "lon": 8.13523,
        "name": "Bühl"
      },
      {
        "lat": 48.16783,
        "lon": 8.62719,
        "name": "Rottweil"
      }
    ],
    "ground_truth": {
      "area_km2": 919603.62,
      "perimeter_km": 4571.78,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Andorra la Vella: (42.5078°, 1.5211°)",
      "  Lebrija: (36.9208°, -6.0753°)",
      "  Great Sankey: (53.3923°, -2.6399°)",
      "  Bühl: (48.6968°, 8.1352°)",
      "  Rottweil: (48.1678°, 8.6272°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4571.78 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 919603.62 km²",
      "FINAL ANSWER: Area: 919603.62 km², Perimeter: 4571.78 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.88758,
        "lon": -6.96807,
        "name": "Aïn Attig"
      },
      {
        "lat": 35.09579,
        "lon": -1.85772,
        "name": "Ghazaouet"
      },
      {
        "lat": 35.16813,
        "lon": -2.93352,
        "name": "Nador"
      },
      {
        "lat": 35.39137,
        "lon": -1.09238,
        "name": "El Malah"
      },
      {
        "lat": 36.57861,
        "lon": 10.85861,
        "name": "Korba"
      }
    ],
    "ground_truth": {
      "area_km2": 41630.11,
      "perimeter_km": 3480.96,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Aïn Attig: (33.8876°, -6.9681°)",
      "  Ghazaouet: (35.0958°, -1.8577°)",
      "  Nador: (35.1681°, -2.9335°)",
      "  El Malah: (35.3914°, -1.0924°)",
      "  Korba: (36.5786°, 10.8586°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3480.96 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 41630.11 km²",
      "FINAL ANSWER: Area: 41630.11 km², Perimeter: 3480.96 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 34.80194,
        "lon": 10.76361,
        "name": "Sakiet ez Zit"
      },
      {
        "lat": 30.97225,
        "lon": 30.95614,
        "name": "Quţūr"
      },
      {
        "lat": 30.03,
        "lon": 31.47,
        "name": "New Cairo"
      },
      {
        "lat": 28.31214,
        "lon": 30.71007,
        "name": "Samālūţ"
      },
      {
        "lat": 27.3126,
        "lon": 30.96987,
        "name": "Manfalūţ"
      }
    ],
    "ground_truth": {
      "area_km2": 379732.41,
      "perimeter_km": 4456.03,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Sakiet ez Zit: (34.8019°, 10.7636°)",
      "  Quţūr: (30.9722°, 30.9561°)",
      "  New Cairo: (30.0300°, 31.4700°)",
      "  Samālūţ: (28.3121°, 30.7101°)",
      "  Manfalūţ: (27.3126°, 30.9699°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4456.03 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 379732.41 km²",
      "FINAL ANSWER: Area: 379732.41 km², Perimeter: 4456.03 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.96179,
        "lon": -96.82917,
        "name": "Addison"
      },
      {
        "lat": 33.40539,
        "lon": -86.81138,
        "name": "Hoover"
      },
      {
        "lat": 29.99409,
        "lon": -90.24174,
        "name": "Kenner"
      }
    ],
    "ground_truth": {
      "area_km2": 173853.28,
      "perimeter_km": 2138.63,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Addison: (32.9618°, -96.8292°)",
      "  Hoover: (33.4054°, -86.8114°)",
      "  Kenner: (29.9941°, -90.2417°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2138.63 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 173853.28 km²",
      "FINAL ANSWER: Area: 173853.28 km², Perimeter: 2138.63 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.76667,
        "lon": 144.96667,
        "name": "Brunswick"
      },
      {
        "lat": -26.65682,
        "lon": 153.07955,
        "name": "Sunshine Coast"
      },
      {
        "lat": -32.92953,
        "lon": 151.7801,
        "name": "Newcastle"
      },
      {
        "lat": -33.88096,
        "lon": 151.07986,
        "name": "Strathfield"
      }
    ],
    "ground_truth": {
      "area_km2": 187263.88,
      "perimeter_km": 2983.52,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Brunswick: (-37.7667°, 144.9667°)",
      "  Sunshine Coast: (-26.6568°, 153.0796°)",
      "  Newcastle: (-32.9295°, 151.7801°)",
      "  Strathfield: (-33.8810°, 151.0799°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2983.52 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 187263.88 km²",
      "FINAL ANSWER: Area: 187263.88 km², Perimeter: 2983.52 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": -37.8149,
        "lon": 144.95052,
        "name": "Docklands"
      },
      {
        "lat": -38.02388,
        "lon": 144.40617,
        "name": "Lara"
      },
      {
        "lat": -36.38047,
        "lon": 145.39867,
        "name": "Shepparton"
      },
      {
        "lat": -28.11694,
        "lon": 153.46584,
        "name": "Palm Beach"
      }
    ],
    "ground_truth": {
      "area_km2": 49331.32,
      "perimeter_km": 2784.41,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Docklands: (-37.8149°, 144.9505°)",
      "  Lara: (-38.0239°, 144.4062°)",
      "  Shepparton: (-36.3805°, 145.3987°)",
      "  Palm Beach: (-28.1169°, 153.4658°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2784.41 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 49331.32 km²",
      "FINAL ANSWER: Area: 49331.32 km², Perimeter: 2784.41 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 30.67307,
        "lon": -8.18087,
        "name": "Aoulouz"
      },
      {
        "lat": 34.30494,
        "lon": -6.30404,
        "name": "Sidi Yahia El Gharb"
      },
      {
        "lat": 35.00044,
        "lon": -5.90378,
        "name": "Ksar El Kebir"
      },
      {
        "lat": 36.12232,
        "lon": 0.89865,
        "name": "Mazouna"
      },
      {
        "lat": 33.35495,
        "lon": 10.50548,
        "name": "Medenine"
      },
      {
        "lat": 32.49094,
        "lon": 3.67347,
        "name": "Ghardaïa"
      }
    ],
    "ground_truth": {
      "area_km2": 523188.9,
      "perimeter_km": 3868.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Aoulouz: (30.6731°, -8.1809°)",
      "  Sidi Yahia El Gharb: (34.3049°, -6.3040°)",
      "  Ksar El Kebir: (35.0004°, -5.9038°)",
      "  Mazouna: (36.1223°, 0.8986°)",
      "  Medenine: (33.3550°, 10.5055°)",
      "  Ghardaïa: (32.4909°, 3.6735°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3868.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 523188.90 km²",
      "FINAL ANSWER: Area: 523188.90 km², Perimeter: 3868.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -26.53333,
        "lon": 29.06667,
        "name": "eMbalenhle"
      },
      {
        "lat": -25.509,
        "lon": 28.064,
        "name": "Mabopane"
      },
      {
        "lat": -20.4943,
        "lon": 27.03479,
        "name": "Tutume"
      },
      {
        "lat": -13.13701,
        "lon": 25.00653,
        "name": "Mufumbwe"
      },
      {
        "lat": -11.66278,
        "lon": 39.55056,
        "name": "Mueda"
      },
      {
        "lat": -22.0,
        "lon": 35.31667,
        "name": "Vilankulo"
      }
    ],
    "ground_truth": {
      "area_km2": 1484359.98,
      "perimeter_km": 5196.65,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  eMbalenhle: (-26.5333°, 29.0667°)",
      "  Mabopane: (-25.5090°, 28.0640°)",
      "  Tutume: (-20.4943°, 27.0348°)",
      "  Mufumbwe: (-13.1370°, 25.0065°)",
      "  Mueda: (-11.6628°, 39.5506°)",
      "  Vilankulo: (-22.0000°, 35.3167°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5196.65 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1484359.98 km²",
      "FINAL ANSWER: Area: 1484359.98 km², Perimeter: 5196.65 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -1.79008,
        "lon": -79.28759,
        "name": "Montalvo"
      },
      {
        "lat": 9.79029,
        "lon": -74.78244,
        "name": "Plato"
      },
      {
        "lat": 3.62057,
        "lon": -75.09415,
        "name": "Natagaima"
      }
    ],
    "ground_truth": {
      "area_km2": 150545.25,
      "perimeter_km": 2828.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Montalvo: (-1.7901°, -79.2876°)",
      "  Plato: (9.7903°, -74.7824°)",
      "  Natagaima: (3.6206°, -75.0941°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2828.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 150545.25 km²",
      "FINAL ANSWER: Area: 150545.25 km², Perimeter: 2828.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 41.18389,
        "lon": -96.03113,
        "name": "La Vista"
      },
      {
        "lat": 44.86219,
        "lon": -93.53079,
        "name": "Chanhassen"
      },
      {
        "lat": 44.38358,
        "lon": -89.81735,
        "name": "Wisconsin Rapids"
      },
      {
        "lat": 40.74899,
        "lon": -74.26126,
        "name": "South Orange"
      }
    ],
    "ground_truth": {
      "area_km2": 359851.62,
      "perimeter_km": 3913.13,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  La Vista: (41.1839°, -96.0311°)",
      "  Chanhassen: (44.8622°, -93.5308°)",
      "  Wisconsin Rapids: (44.3836°, -89.8174°)",
      "  South Orange: (40.7490°, -74.2613°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3913.13 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 359851.62 km²",
      "FINAL ANSWER: Area: 359851.62 km², Perimeter: 3913.13 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 40.32605,
        "lon": -3.51089,
        "name": "Rivas-Vaciamadrid"
      },
      {
        "lat": 40.28106,
        "lon": -7.50504,
        "name": "Covilhã"
      },
      {
        "lat": 52.33964,
        "lon": 4.96256,
        "name": "Diemen"
      },
      {
        "lat": 51.83167,
        "lon": 4.6875,
        "name": "Papendrecht"
      },
      {
        "lat": 50.89559,
        "lon": 7.18175,
        "name": "Rösrath"
      }
    ],
    "ground_truth": {
      "area_km2": 386181.35,
      "perimeter_km": 3679.59,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Rivas-Vaciamadrid: (40.3261°, -3.5109°)",
      "  Covilhã: (40.2811°, -7.5050°)",
      "  Diemen: (52.3396°, 4.9626°)",
      "  Papendrecht: (51.8317°, 4.6875°)",
      "  Rösrath: (50.8956°, 7.1818°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3679.59 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 386181.35 km²",
      "FINAL ANSWER: Area: 386181.35 km², Perimeter: 3679.59 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 36.13968,
        "lon": -120.36015,
        "name": "Coalinga"
      },
      {
        "lat": 40.56217,
        "lon": -111.92966,
        "name": "South Jordan"
      },
      {
        "lat": 47.86602,
        "lon": -122.1551,
        "name": "Silver Firs"
      },
      {
        "lat": 38.9556,
        "lon": -90.18678,
        "name": "Godfrey"
      },
      {
        "lat": 40.01499,
        "lon": -105.27055,
        "name": "Boulder"
      },
      {
        "lat": 39.37221,
        "lon": -104.85609,
        "name": "Castle Rock"
      }
    ],
    "ground_truth": {
      "area_km2": 2518898.03,
      "perimeter_km": 7559.99,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Coalinga: (36.1397°, -120.3602°)",
      "  South Jordan: (40.5622°, -111.9297°)",
      "  Silver Firs: (47.8660°, -122.1551°)",
      "  Godfrey: (38.9556°, -90.1868°)",
      "  Boulder: (40.0150°, -105.2706°)",
      "  Castle Rock: (39.3722°, -104.8561°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 7559.99 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 2518898.03 km²",
      "FINAL ANSWER: Area: 2518898.03 km², Perimeter: 7559.99 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 38.34517,
        "lon": -0.48149,
        "name": "Alicante"
      },
      {
        "lat": 40.37846,
        "lon": -3.6739,
        "name": "Entrevías"
      },
      {
        "lat": 53.50291,
        "lon": -1.3458,
        "name": "Wath upon Dearne"
      },
      {
        "lat": 50.85568,
        "lon": 0.58009,
        "name": "Hastings"
      },
      {
        "lat": 52.01954,
        "lon": 4.42946,
        "name": "Pijnacker"
      }
    ],
    "ground_truth": {
      "area_km2": 502804.79,
      "perimeter_km": 4011.72,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Alicante: (38.3452°, -0.4815°)",
      "  Entrevías: (40.3785°, -3.6739°)",
      "  Wath upon Dearne: (53.5029°, -1.3458°)",
      "  Hastings: (50.8557°, 0.5801°)",
      "  Pijnacker: (52.0195°, 4.4295°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4011.72 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 502804.79 km²",
      "FINAL ANSWER: Area: 502804.79 km², Perimeter: 4011.72 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 33.74002,
        "lon": -116.93891,
        "name": "East Hemet"
      },
      {
        "lat": 34.86526,
        "lon": -120.436,
        "name": "Orcutt"
      },
      {
        "lat": 37.72855,
        "lon": -122.38107,
        "name": "Bayview-Hunters Point"
      },
      {
        "lat": 32.73569,
        "lon": -97.10807,
        "name": "Arlington"
      },
      {
        "lat": 25.74167,
        "lon": -100.30222,
        "name": "San Nicolás de los Garza"
      }
    ],
    "ground_truth": {
      "area_km2": 1239060.64,
      "perimeter_km": 5731.01,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  East Hemet: (33.7400°, -116.9389°)",
      "  Orcutt: (34.8653°, -120.4360°)",
      "  Bayview-Hunters Point: (37.7285°, -122.3811°)",
      "  Arlington: (32.7357°, -97.1081°)",
      "  San Nicolás de los Garza: (25.7417°, -100.3022°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5731.01 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1239060.64 km²",
      "FINAL ANSWER: Area: 1239060.64 km², Perimeter: 5731.01 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": -20.24056,
        "lon": -56.37833,
        "name": "Miranda"
      },
      {
        "lat": -23.535,
        "lon": -47.26194,
        "name": "Alumínio"
      },
      {
        "lat": -23.84861,
        "lon": -50.18778,
        "name": "Ibaiti"
      }
    ],
    "ground_truth": {
      "area_km2": 68265.78,
      "perimeter_km": 2062.6,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Miranda: (-20.2406°, -56.3783°)",
      "  Alumínio: (-23.5350°, -47.2619°)",
      "  Ibaiti: (-23.8486°, -50.1878°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2062.60 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 68265.78 km²",
      "FINAL ANSWER: Area: 68265.78 km², Perimeter: 2062.60 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 40.39061,
        "lon": -3.64824,
        "name": "Portazgo"
      },
      {
        "lat": 48.96164,
        "lon": 10.13173,
        "name": "Ellwangen"
      },
      {
        "lat": 46.38318,
        "lon": 6.23955,
        "name": "Nyon"
      }
    ],
    "ground_truth": {
      "area_km2": 35667.56,
      "perimeter_km": 2891.32,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Portazgo: (40.3906°, -3.6482°)",
      "  Ellwangen: (48.9616°, 10.1317°)",
      "  Nyon: (46.3832°, 6.2396°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 2891.32 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 35667.56 km²",
      "FINAL ANSWER: Area: 35667.56 km², Perimeter: 2891.32 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "5-sided",
    "vertices": [
      {
        "lat": 32.43501,
        "lon": 13.6332,
        "name": "Tarhuna"
      },
      {
        "lat": 31.19688,
        "lon": 31.5243,
        "name": "Shirbīn"
      },
      {
        "lat": 30.15293,
        "lon": 31.31501,
        "name": "Al Khuşūş"
      },
      {
        "lat": 25.87198,
        "lon": 32.75585,
        "name": "Jarājūs"
      },
      {
        "lat": 19.61745,
        "lon": 37.21644,
        "name": "Port Sudan"
      }
    ],
    "ground_truth": {
      "area_km2": 888228.52,
      "perimeter_km": 5884.54,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (5 vertices)",
      "  Tarhuna: (32.4350°, 13.6332°)",
      "  Shirbīn: (31.1969°, 31.5243°)",
      "  Al Khuşūş: (30.1529°, 31.3150°)",
      "  Jarājūs: (25.8720°, 32.7559°)",
      "  Port Sudan: (19.6175°, 37.2164°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 5884.54 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 888228.52 km²",
      "FINAL ANSWER: Area: 888228.52 km², Perimeter: 5884.54 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 38.67851,
        "lon": -121.22578,
        "name": "Orangevale"
      },
      {
        "lat": 45.53929,
        "lon": -122.38731,
        "name": "Troutdale"
      },
      {
        "lat": 31.30862,
        "lon": -110.94217,
        "name": "Nogales"
      }
    ],
    "ground_truth": {
      "area_km2": 341436.34,
      "perimeter_km": 3877.95,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  Orangevale: (38.6785°, -121.2258°)",
      "  Troutdale: (45.5393°, -122.3873°)",
      "  Nogales: (31.3086°, -110.9422°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3877.95 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 341436.34 km²",
      "FINAL ANSWER: Area: 341436.34 km², Perimeter: 3877.95 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": 33.24528,
        "lon": 131.69165,
        "name": "Tsurusaki"
      },
      {
        "lat": 31.42813,
        "lon": 119.48353,
        "name": "Licheng"
      },
      {
        "lat": 40.04068,
        "lon": 124.33525,
        "name": "Langtoucun"
      },
      {
        "lat": 38.70882,
        "lon": 141.15578,
        "name": "Tome"
      },
      {
        "lat": 35.67452,
        "lon": 139.48216,
        "name": "Fuchū"
      },
      {
        "lat": 34.86437,
        "lon": 134.552,
        "name": "Tatsunochō-tominaga"
      }
    ],
    "ground_truth": {
      "area_km2": 1149238.92,
      "perimeter_km": 4811.82,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Tsurusaki: (33.2453°, 131.6917°)",
      "  Licheng: (31.4281°, 119.4835°)",
      "  Langtoucun: (40.0407°, 124.3353°)",
      "  Tome: (38.7088°, 141.1558°)",
      "  Fuchū: (35.6745°, 139.4822°)",
      "  Tatsunochō-tominaga: (34.8644°, 134.5520°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4811.82 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1149238.92 km²",
      "FINAL ANSWER: Area: 1149238.92 km², Perimeter: 4811.82 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "4-sided",
    "vertices": [
      {
        "lat": 43.53692,
        "lon": 6.46458,
        "name": "Draguignan"
      },
      {
        "lat": 49.92139,
        "lon": 8.48255,
        "name": "Groß-Gerau"
      },
      {
        "lat": 53.48097,
        "lon": -2.24555,
        "name": "Manchester City Centre"
      },
      {
        "lat": 50.91741,
        "lon": 34.79906,
        "name": "Sumy"
      }
    ],
    "ground_truth": {
      "area_km2": 1753884.32,
      "perimeter_km": 6349.87,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (4 vertices)",
      "  Draguignan: (43.5369°, 6.4646°)",
      "  Groß-Gerau: (49.9214°, 8.4825°)",
      "  Manchester City Centre: (53.4810°, -2.2456°)",
      "  Sumy: (50.9174°, 34.7991°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 6349.87 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1753884.32 km²",
      "FINAL ANSWER: Area: 1753884.32 km², Perimeter: 6349.87 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "6-sided",
    "vertices": [
      {
        "lat": -9.78333,
        "lon": 16.43333,
        "name": "Cangandala"
      },
      {
        "lat": -8.57848,
        "lon": 13.66425,
        "name": "Caxito"
      },
      {
        "lat": -5.83861,
        "lon": 13.46306,
        "name": "Matadi"
      },
      {
        "lat": 6.32229,
        "lon": 19.07922,
        "name": "Dekoa"
      },
      {
        "lat": -6.22149,
        "lon": 23.39254,
        "name": "Miabi"
      },
      {
        "lat": -8.23619,
        "lon": 19.52566,
        "name": "Cuilo"
      }
    ],
    "ground_truth": {
      "area_km2": 1038628.62,
      "perimeter_km": 4463.74,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (6 vertices)",
      "  Cangandala: (-9.7833°, 16.4333°)",
      "  Caxito: (-8.5785°, 13.6642°)",
      "  Matadi: (-5.8386°, 13.4631°)",
      "  Dekoa: (6.3223°, 19.0792°)",
      "  Miabi: (-6.2215°, 23.3925°)",
      "  Cuilo: (-8.2362°, 19.5257°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 4463.74 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 1038628.62 km²",
      "FINAL ANSWER: Area: 1038628.62 km², Perimeter: 4463.74 km"
    ]
  },
  {
    "task": "area_perimeter",
    "polygon_type": "3-sided",
    "vertices": [
      {
        "lat": 32.57286,
        "lon": -6.01947,
        "name": "El Ksiba"
      },
      {
        "lat": 36.65393,
        "lon": 3.98143,
        "name": "Tirmitine"
      },
      {
        "lat": 36.82657,
        "lon": 10.08974,
        "name": "Douar Hicher"
      }
    ],
    "ground_truth": {
      "area_km2": 93872.72,
      "perimeter_km": 3109.81,
      "tolerance_percent": 5.0
    },
    "reasoning_steps": [
      "Step 1: Identify polygon vertices (3 vertices)",
      "  El Ksiba: (32.5729°, -6.0195°)",
      "  Tirmitine: (36.6539°, 3.9814°)",
      "  Douar Hicher: (36.8266°, 10.0897°)",
      "Step 2: Calculate perimeter",
      "  Sum distances between consecutive vertices using Haversine",
      "  Perimeter = 3109.81 km",
      "Step 3: Calculate area using spherical excess formula",
      "  Area on sphere = R² × E, where E is spherical excess",
      "  Area = 93872.72 km²",
      "FINAL ANSWER: Area: 93872.72 km², Perimeter: 3109.81 km"
    ]
  }
]