Search is not available for this dataset
data_source stringclasses 10
values | prompt listlengths 2 2 | ability stringclasses 2
values | reward_model dict | extra_info dict | ground_truth stringlengths 1 79.2M | messages listlengths 1 1 | dataset stringclasses 1
value |
|---|---|---|---|---|---|---|---|
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-268^{\\circ}\\mathrm{C}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -268^{\circ}\mathrm{C} | [
{
"content": "The liquefaction temperatures (at standard atmospheric pressure) of several gases are shown in the table below. Find the gas with the lowest liquefaction temperature.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0 | [
{
"content": "If the complex number $\\left(m^{2}-3m\\right)+\\left(m^{2}-5m+6\\right)i$ is purely imaginary, calculate the value of the real number $m$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 6 | [
{
"content": "What is the remainder when $3^{100} + 5$ is divided by $11$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 40 | [
{
"content": "Determine the number of quadruples of natural numbers \\((a, b, c, d)\\) satisfying \\(a \\cdot b \\cdot c \\cdot d = 98\\).\n\nNote: \\((98, 1, 1, 1)\\) and \\((1, 1, 98, 1)\\) are considered different quadruples.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | PRIME-Eurus-2-RL-Data |
numina_aops_forum | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "20^{1011} \\times 5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 20^{1011} \times 5 | [
{
"content": "We say that a positive integer is guarani if the sum of the number with its reverse is a number that only has odd digits. For example, $249$ and $30$ are guarani, since $249 + 942 = 1191$ and $30 + 03 = 33$ .\na) How many $2021$ -digit numbers are guarani?\nb) How many $2023$ -digit numbe... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{2} | [
{
"content": "Given $2\\sin (π-x)+1=0$, find the value of $\\cos 2x$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "781",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 781 | [
{
"content": "For each positive integer $n$, let $f(n)$ be the sum of the digits in the base-five representation of $n$ and let $g(n)$ be the sum of the digits in the base-seven representation of $f(n)$. For example, if $f(2020)$ is calculated in base five and then $g(2020)$ is the sum of the digits in the base... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\dfrac{10\\pi}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \dfrac{10\pi}{3} | [
{
"content": "The length of the arc of a circle with a radius of $2$ and a central angle of $300^\\circ$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(x-5)^2+(y-5)^2=25 \\quad \\text{or} \\quad (x-1)^2+(y-1)^2=1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (x-5)^2+(y-5)^2=25 \quad \text{or} \quad (x-1)^2+(y-1)^2=1 | [
{
"content": "Write the equation of the circle that is tangent to the coordinate axes and passes through the point \\(A(2, 1)\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "[18, \\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | [18, \infty) | [
{
"content": "Find all values of \\( x > 6 \\) which satisfy\n\\[\n\\sqrt{x - 6 \\sqrt{x - 9}} + 3 = \\sqrt{x + 6 \\sqrt{x - 9}} - 3.\n\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3 | [
{
"content": "Let $Q$ be a point within triangle $DEF$ such that \n\\[\\overrightarrow{QD} + 3 \\overrightarrow{QE} + 2 \\overrightarrow{QF} = \\mathbf{0}.\\]\nFind the ratio of the area of triangle $DEF$ to the area of triangle $DQF.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-\\frac{26}{9}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{26}{9} | [
{
"content": "Compute \\(a^2 + b^2 + c^2\\), given that \\(a\\), \\(b\\), and \\(c\\) are the roots of\n\\[\n3x^3 - 2x^2 + 5x + 15 = 0.\n\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "[ \\frac {2π}{3},π]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | [ \frac {2π}{3},π] | [
{
"content": "Given the function $f(x)=\\sin (2x+φ)$, where $φ$ is a real number, if $f(x)\\leqslant |f( \\frac {π}{6})|$ holds for all $x\\in R$, and $f( \\frac {π}{2}) > f(π)$.\n$(1)$ Find the analytic expression of the function $f(x)$;\n$(2)$ Find the monotonically decreasing interval of the function $f(x)$ ... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "540",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 540 | [
{
"content": "The shaded rectangle in square PQRS has a side length of 21 and a side length that is x. If the perimeter of each of the four non-overlapping rectangles is the same, calculate the area of the shaded rectangle.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4.5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4.5 | [
{
"content": "The complete graph of $y=g(x)$, which consists of four line segments, is shown below. Find the sum of the $x$-coordinates of all points where $g(x) = 2.5$. The equations of the line segments, from left to right, are:\n1. $y = 3x + 6$ for $-4 \\leq x \\leq -2$,\n2. $y = -x + 2$ for $-2 < x \\leq 0$... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\text{If }f(x)=x^3,\\text{ then }f'(x)=3x^2. We have",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \text{If }f(x)=x^3,\text{ then }f'(x)=3x^2. We have | [
{
"content": "Given that $x$ is a solution to the equation $f'(x)=0$, determine the relationship between $x$ and the critical points of the function $f(x)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5 | [
{
"content": "Let $\\left\\{a_{n}\\right\\}$ be an arithmetic sequence with the sum of its first $n$ terms denoted as $S_{n}$. If $S_{17}=255$ and $a_{10}=20$, find the common difference of the sequence $\\left\\{a_{n}\\right\\}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x_1 = 1,\\ x_2 = 2,\\ x_3 = 3,\\ x_4 = 4,\\ x_5 = -4,\\ x_6 = -3,\\ x_7 = -2,\\ x_8 = -1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x_1 = 1,\ x_2 = 2,\ x_3 = 3,\ x_4 = 4,\ x_5 = -4,\ x_6 = -3,\ x_7 = -2,\ x_8 = -1 | [
{
"content": "Solve the system of equations:\n$$\n\\left\\{\\begin{array}{l}\nx_{1} + x_{2} + x_{3} = 6, \\\\\nx_{2} + x_{3} + x_{4} = 9, \\\\\nx_{3} + x_{4} + x_{5} = 3, \\\\\nx_{4} + x_{5} + x_{6} = -3, \\\\\nx_{5} + x_{6} + x_{7} = -9, \\\\\nx_{6} + x_{7} + x_{8} = -6, \\\\\nx_{7} + x_{8} + x_{1} = -2, \\\\\... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4 | [
{
"content": "How many perfect squares less than $100$ are divisible by $4$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "342",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 342 | [
{
"content": "Evaluate the expression: $(3 \\times 4 \\times 5 \\times 6) \\left(\\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6}\\right)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1211",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1211 | [
{
"content": "Given that a store has introduced 3,000 bags of milk powder, to check whether the melamine content exceeds the standard, a systematic sampling method is used to extract 150 bags for inspection. If the first sampled bag's number is 11, determine the bag number of the 61st group sampled.\n\nPresent ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "5040",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5040 | [
{
"content": "Find the greatest common divisor of \\(7!\\) and \\(8!\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_aops_forum | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{8}{9}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{8}{9} | [
{
"content": "Circle $o$ contains the circles $m$ , $p$ and $r$ , such that they are tangent to $o$ internally and any two of them are tangent between themselves. The radii of the circles $m$ and $p$ are equal to $x$ . The circle $r$ has radius $1$ and passes through the center of the circle ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{150 \\sqrt{2}}{29}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{150 \sqrt{2}}{29} | [
{
"content": "Compute the distance between the parallel lines given by\n\\[\\begin{pmatrix} 3 \\\\ -4 \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ -5 \\end{pmatrix}\\]\nand\n\\[\\begin{pmatrix} -1 \\\\ 1 \\end{pmatrix} + s \\begin{pmatrix} 2 \\\\ -5 \\end{pmatrix}.\\]\n\nPresent the answer in LaTex format: \\boxe... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3 | [
{
"content": "There are 12 trams circulating on a ring line in one direction at the same speed and equal intervals. How many trams need to be added so that, at the same speed, the intervals between the trams are reduced by one fifth?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{l_1}{l_2} = \\sqrt{\\frac{d_2 \\alpha_2}{d_1 \\alpha_1}}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{l_1}{l_2} = \sqrt{\frac{d_2 \alpha_2}{d_1 \alpha_1}} | [
{
"content": "Two homogeneous rods with equal cross-sectional areas, different densities, and different coefficients of expansion are welded together in such a way that the system's center of gravity remains unchanged despite thermal expansion. How do the lengths of the rods relate to each other?\n\nPresent the... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-21600",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -21600 | [
{
"content": "In the expansion of \\((-xy + 2x + 3y - 6)^6\\), what is the coefficient of \\(x^4 y^3\\)? (Answer with a specific number)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "700",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 700 | [
{
"content": "Let x be the number of yellow coins collected, let y be the number of red coins collected, and let z be the number of blue coins collected. Set up and solve the system of equations: x + y + z = 2800, 3y + 5z = 7800, and z = y + 200.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5 | [
{
"content": "Mouse Jerry decided to give Cat Tom a birthday pie in the shape of an $8 \\times 8$ square. He placed fish in three pieces marked with the letter \"P,\" sausage in two pieces marked with the letter \"K,\" and both fish and sausage in one piece, which he did not mark (all other pieces are without f... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "0.97",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0.97 | [
{
"content": "A farm introduced a batch of new vegetable seeds. Before sowing, germination tests were conducted under the same conditions, and the results are shown in the table below:\n\n| Number of Seeds Tested | 500 | 1000 | 2000 | 10000 | 20000 |\n|------------------------|-----|------|------|-------|------... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \sqrt{3} | [
{
"content": "Given vectors $\\overrightarrow{m}=(\\sin (x-\\frac{\\pi }{6}),\\cos x)$ and $\\overrightarrow{n}=(\\cos x,\\cos x)$, if the function $f(x)=\\overrightarrow{m}\\cdot \\overrightarrow{n}-\\frac{1}{4}$.\n\n$(1)$ Find the range of $f(x)$ when $x\\in\\left[-\\frac{\\pi }{4},\\frac{\\pi }{2} \\right]$;... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "x = C \\cdot e^{y^2 / x}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | x = C \cdot e^{y^2 / x} | [
{
"content": "Solve the equation \\(\\left(x + y^{2}\\right) \\, dx - 2xy \\, dy = 0\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{4} | [
{
"content": "A running competition on an unpredictable distance is conducted as follows. On a round track, two points \\( A \\) and \\( B \\) are chosen randomly (with the help of a spinning arrow), after which the athletes run from \\( A \\) to \\( B \\) along the shorter arc. A spectator bought a ticket to t... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1-\\frac{1}{2}\\ln 2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1-\frac{1}{2}\ln 2 | [
{
"content": "Given the functions $f(x)=e^{2x}$ and $g(x)=\\ln x+ \\frac{1}{2}$, for $\\forall a \\in \\mathbb{R}$, $\\exists b \\in (0,+\\infty)$, such that $f(a)=g(b)$, determine the minimum value of $b-a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "5000",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5000 | [
{
"content": "A club has $5$ members from each of $4$ different schools, for a total of $20$ members. Calculate the number of possible ways to arrange a presidency meeting under the following conditions:\ni. The club must choose one of the $4$ schools at which to host the meeting.\nii. The host school sends $3$... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8 | [
{
"content": "Determine the values of $a$, $b$, and $c$ such that the equation $\\cos^2 x + \\cos^2 2x + \\cos^2 3x + \\cos^2 4x = 2$ can be reduced to $\\sin a x \\sin b x \\sin c x = 0$ for some positive integers $a$, $b$, and $c$. Find $a + b + c$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 29 | [
{
"content": "Find the integer $n$, $0 \\le n \\le 180$, such that $\\cos n^\\circ = \\cos 331^\\circ$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "H = \\left( \\frac{101}{33}, \\frac{95}{33}, \\frac{47}{33} \\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | H = \left( \frac{101}{33}, \frac{95}{33}, \frac{47}{33} \right) | [
{
"content": "Find the orthocenter of triangle $ABC$, where $A = (2, 3, -1)$, $B = (6, -1, 2)$, and $C = (4, 5, 4)$ in coordinate space.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "- \\frac{2}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | - \frac{2}{3} | [
{
"content": "Let the function $y=f(x)$ be differentiable at $x=x_0$, and $\\lim\\limits_{\\Delta x \\to 0} \\frac{f(x_0-3\\Delta x)-f(x_0)}{2\\Delta x} = 1$, then find the value of $f'(x_0)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "What is the remainder when $11^{2010}$ is divided by $50$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "225",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 225 | [
{
"content": "Simplify $\\sqrt{3 \\cdot 5} \\cdot \\sqrt{5^3 \\cdot 3^3}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{3} | [
{
"content": "Xiaoming forgot how to write $egg$ and only remembered there were three letters $e$, $g$, $g$. He randomly wrote one of them. Calculate the probability that he wrote it correctly.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "7 \\cdot 3^{49}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 7 \cdot 3^{49} | [
{
"content": "How many 100-digit natural numbers are there, each digit of which is even and the difference between any two adjacent digits is $2$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{1}{4} | [
{
"content": "The maximum value of the function $y=x-x^2$ ($x\\in \\mathbb{R}$) is ____.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac { \\sqrt {5}}{10}x+ \\frac { \\sqrt {3}}{6}y=1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac { \sqrt {5}}{10}x+ \frac { \sqrt {3}}{6}y=1 | [
{
"content": "Given a line $\\sqrt {6}x+2y-2 \\sqrt {6}=0$ passes through a vertex E and a focus F of the ellipse $\\frac {x^{2}}{a^{2}}+ \\frac {y^{2}}{b^{2}}=1$ ($a>b>0$),\n(1) Find the standard equation of the ellipse;\n(2) Find the equation of the tangent line to the ellipse passing through point P($\\sqrt ... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\text{②③}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \text{②③} | [
{
"content": "There are 13 doctors, among which there are 6 female doctors. Now, 5 doctors are selected to form a medical team to go to the disaster area. If the medical team must have at least 2 male doctors and at most 3 female doctors, let the number of different methods of selection be $N$. Then, among the ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "10001000111_2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 10001000111_2 | [
{
"content": "Find the product of $101101_2$ and $1101_2$. Express your answer in base $2$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-5, -4, -3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -5, -4, -3 | [
{
"content": "Determine how many integers satisfy the following inequalities:\n\\[\n\\begin{array}{cccc}\n(1) & -5x & \\geq & 3x+11 \\\\\n(2) & -3x & \\leq & 15 \\\\\n(3) & -6x & \\geq & 4x+23\n\\end{array}\n\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{2}{9}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{2}{9} | [
{
"content": "When rolling two fair 6-sided dice, what is the probability that the sum of the numbers rolled is either 5 or 9?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\{x|x < -\\frac{1}{3}\\text{ or } x > \\frac{1}{2}\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \{x|x < -\frac{1}{3}\text{ or } x > \frac{1}{2}\} | [
{
"content": "Given the inequality $(3x+1)(2x-1) > 0$, find the solution set.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 12 | [
{
"content": "How many positive four-digit integers of the form $\\_\\_20$ are divisible by 40?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2-2i",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2-2i | [
{
"content": "The equation $x^{2}+(4+i)x+4+ai=0$ ($a\\in\\mathbb{R}$) has a real root $b$, and $z=a+bi$, find the value of $z$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\dfrac{π}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \dfrac{π}{3} | [
{
"content": "Given that $\\cos α= \\dfrac {1}{7}$ and $\\cos (α-β)= \\dfrac {13}{14}$, with $0 < β < α < \\dfrac {π}{2}$, find the value of $\\tan 2α$ and the value of $β$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "You have a rectangular prism box with length $x+6$ units, width $x-6$ units, and height $x^2 + 36$ units. For how many positive integer values of $x$ is the volume of the box less than 800 units?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2\\sqrt{65}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2\sqrt{65} | [
{
"content": "A circle with center $O$ has radius $10$ units and circle $P$ has radius $4$ units. The circles are externally tangent to each other at point $Q$. Segment $TS$ is the common external tangent to circle $O$ and circle $P$ at points $T$ and $S$, respectively. What is the length of segment $OS$? Expr... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\sqrt{3}}{4} | [
{
"content": "The base of a right prism is a regular hexagon with vertices $A_1, \\ldots, A_6$ and the top base has vertices $B_1, \\ldots, B_6$ with center $O$. The side edge $A_{1} B_{1}$ is equal to the diagonal $A_{1} A_{3}$. On the side edges $A_{1} B_{1}$, $A_{3} B_{3}$, and $A_{5} B_{5}$, consider points... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "m\\geqslant \\frac {5}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | m\geqslant \frac {5}{4} | [
{
"content": "Given the functions $f(x)=x^{3}-3x+1$ and $g(x)=( \\frac {1}{2})^{x}-m$, if for $\\forall x_{1}\\in[-1,3]$, $\\exists x_{2}\\in[0,2]$, $f(x_{1})\\geqslant g(x_{2})$, then the range of the real number $m$ is \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "Given the function $f(x)=\\cos x-\\sin x$, find the value of $f''\\left(\\frac{\\pi}{2}\\right)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 7 | [
{
"content": "Given $M=\\{1,2,3,4\\}$, $N=\\{2,3,4,5\\}$, and $P=\\{x|x=a+b, a\\in M, b\\in N\\}$, calculate the number of elements in set $P$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{3}{2} | [
{
"content": "Given a quadratic function about $x$, $y=a\\left(x-m\\right)^{2}+a\\left(x-m\\right)$, where $a$ and $m$ are constants with $a \\gt 0$ and $m \\gt 0$. The graph of the function intersects the $x$-axis at points $A$ and $B$. Please complete the following questions:<br/>$(1)$ The length of segment $... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2240",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2240 | [
{
"content": "In the multiplication example written on the blackboard, the bully Petya changed two digits. The resulting example is 4$\\cdot$5$\\cdot$4$\\cdot$5$\\cdot$4 = 2247. Restore the original example.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 48 | [
{
"content": "There are 2 boys and 3 girls, a total of 5 students standing in a row. If boy A does not stand at either end, and exactly 2 of the 3 girls stand next to each other, then the number of different arrangements is\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 30 | [
{
"content": "Josef and Timothy play a game in which Josef picks an integer between 1 and 1200 inclusive, and Timothy divides 1200 by that integer and states whether or not the quotient is an integer. How many integers could Josef pick such that Timothy's quotient is an integer?\n\nPresent the answer in LaTex f... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "t + 15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | t + 15 | [
{
"content": "David works at a widget factory where on Monday he typically produces $w$ widgets per hour for $t$ hours. Feeling even more tired on Tuesday, he cuts back his working hours by 3 but increases his production rate by 5 widgets per hour compared to Monday. Given that $w = 2t$, determine how many more... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "a^{\\frac{2}{3}}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | a^{\frac{2}{3}} | [
{
"content": "Given $a \\gt 0$, express $\\sqrt{a•\\sqrt[3]{a}}$ in the form of a rational exponent. The result is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 15 | [
{
"content": "Given the initial percentage of girls in the group is $50\\%$, three girls leave and three boys join the group, resulting in a $40\\%$ female group. Find the initial number of girls in the group.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2530.5 \\text{ yuan}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2530.5 \text{ yuan} | [
{
"content": "Technology changes life, and online sales are becoming increasingly popular. Many agricultural businesses use online sales to market their products and achieve prosperity. Xiao Hong sells the apples grown in her own home online, planning to sell $100$ kilograms per day. The actual daily sales volu... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 2 | [
{
"content": "Given $S(n)$ is the sum of the remainders when $n$ is divided by each integer from $3$ to $12$, and $D(n) = S(n) - S(n-1)$, find the number of two-digit positive integers $n$ such that $D(n) = 0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{15}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{15}{4} | [
{
"content": "Compute the following expressions:\n\\begin{align*}\n(1) \\sqrt{(2 \\frac{1}{4})} - (-9.6)^{0} - (3 \\frac{3}{8})^{-\\frac{2}{3}} + (1.5)^{-2}; \\\\\n(2) \\log_{3} \\frac{427}{3} + \\log 25 + \\log 4 + 7^{\\log_{7}2}.\n\\end{align*}\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "60°",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 60° | [
{
"content": "In triangle ABC, if $(a+b+c)(b+c-a)=3bc$, then $A$ equals \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 1 | [
{
"content": "Given the function $y=f(x)$ satisfies $f(xy) = f(x)f(y)$, and $f(0) \\neq 0$, calculate the value of $f(2009)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-18, -9, -6, -3, -2, -1, 1, 2, 3, 6, 9, 18",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -18, -9, -6, -3, -2, -1, 1, 2, 3, 6, 9, 18 | [
{
"content": "A polynomial with integer coefficients is of the form\n\\[x^3 + a_2 x^2 - 7x - 18 = 0.\\]\nEnter all the possible integer roots of this polynomial, separated by commas.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 15 | [
{
"content": "A rectangular room measures 18 feet in length and 9 feet in width. How many square meters of carpet are needed to cover the room's floor?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 60^\circ | [
{
"content": "In the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, what is the measure of the dihedral angle $A-B D_{1}-A_{1}$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3 | [
{
"content": "For how many integers \\( n \\) is it true that \\( \\sqrt{n+2} \\leq \\sqrt{6n - 8} < \\sqrt{3n + 7} \\)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{\\sqrt{232}}{14}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{\sqrt{232}}{14} | [
{
"content": "Let $\\triangle DEF$ have side lengths $DE=20$, $DF=21$, and $EF=29$. There are two circles located inside $\\angle D$. One of these is tangent to rays $\\overline{DE}$, $\\overline{DF}$ and segment $\\overline{EF}$. The other circle is tangent to the extension of $\\overline{DE}$ and $\\overline{... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "B) 10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | B) 10 | [
{
"content": "Each of the 60 students in the ninth grade at Hudson High School has one dog, one cat, one bird, or any combination of these three pets. Thirty-five students have a dog, 45 students have a cat, and 10 students have a bird. All students that have a bird also have at least one other pet. How many st... | PRIME-Eurus-2-RL-Data |
numina_aops_forum | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3004",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3004 | [
{
"content": "The number $734{,}851{,}474{,}594{,}578{,}436{,}096$ is equal to $n^6$ for some positive integer $n$ . What is the value of $n$ ?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "3660",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 3660 | [
{
"content": "The development of new energy can effectively solve the energy shortage and environmental pollution caused by the use of traditional energy sources in China. The introduction of national new energy policies has brought spring to the new energy industry. It is known that a new energy company in Zhe... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\left(a-1, 2^k a-1\\right) \\text{ and } \\left(2^k a-1, a-1\\right) \\text{ for } a \\geq 2 \\text{ and } k \\geq 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \left(a-1, 2^k a-1\right) \text{ and } \left(2^k a-1, a-1\right) \text{ for } a \geq 2 \text{ and } k \geq 0 | [
{
"content": "Art and Ben play a game while sharing an \\( m \\times n \\) chocolate bar. They take turns breaking the bar into two rectangular pieces along one of the lines and eating the smaller piece. (If the two pieces are equal, they can choose which piece to eat.) Whoever is left with the last \\( 1 \\tim... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(k(k+1), 3k + 1), \\, k \\in \\mathbb{Z}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (k(k+1), 3k + 1), \, k \in \mathbb{Z} | [
{
"content": "Solve the equation \\( 9x + 2 = y(y + 1) \\) in integers.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-\\frac{\\sqrt{7}}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -\frac{\sqrt{7}}{3} | [
{
"content": "Given that \\\\(\\alpha\\\\) and \\\\(\\beta\\\\) are acute angles, and \\\\(\\sin \\alpha - \\sin \\beta = -\\frac{1}{2}\\\\), \\\\(\\cos \\alpha - \\cos \\beta = \\frac{1}{2}\\\\), find \\\\(\\tan (\\alpha - \\beta)\\\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\frac{2}{15}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \frac{2}{15} | [
{
"content": "Four red beads, two white beads, and one green bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?\nA) $\\frac{1}{15}$\nB) $\\frac{2}{15}$\nC) $\\frac{1}{7}$\nD) $\\frac{1}{30}$\nE) $\\frac{1}{21}$\n\nPresent the answer in LaTex form... | PRIME-Eurus-2-RL-Data |
numina_amc_aime | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 8 | [
{
"content": "Given the product of two whole numbers is 24 and their sum is 11, determine the value of the larger number.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-2i",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -2i | [
{
"content": "Given the complex number $z=1-\\sqrt{2}i$, find the value of $\\frac{4i}{1-z\\overset{ .}{z}}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "y + x + \\sqrt{3} = 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | y + x + \sqrt{3} = 0 | [
{
"content": "The equation of the line that passes through the point $P(\\sqrt{3}, -2\\sqrt{3})$ and has an inclination angle of 135° is to be determined.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\sqrt{2} + 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \sqrt{2} + 1 | [
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are respectively $a$, $b$, and $c$. It is given that $\\frac{-b + \\sqrt{2}c}{\\cos B} = \\frac{a}{\\cos A}$, \n$(I)$ Find the size of angle $A$; \n$(II)$ If $a=2$, find the maximum value of the area $S$.\n\nPresent the answer i... | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "||PA|-|PB||=4\\sqrt{3}-2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | ||PA|-|PB||=4\sqrt{3}-2 | [
{
"content": "Given a curve C with the polar coordinate equation ρ$^2$cos2θ=a$^2$ (where a∈R and a is a constant), and a line l with the parameter equation x=2+$\\frac{\\sqrt{3}}{2}$t (t is the parameter) that passes through point P(2,1) with a slope angle of 30°.\n\n1. Find the Cartesian equation of curve C an... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 10 | [
{
"content": "Find the number of solutions to the equation\n\\[\\tan (3 \\pi \\cos^3 \\theta) = \\cot (3 \\pi \\sin^3 \\theta)\\]\nwhere $\\theta \\in (0, \\pi).$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "323",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 323 | [
{
"content": "How many whole numbers between 1 and 500 do not contain the digit 2?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "\\dfrac{1}{2}+ \\dfrac{1}{2}i",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \dfrac{1}{2}+ \dfrac{1}{2}i | [
{
"content": "If $i$ is the imaginary unit, then $\\dfrac{i}{1+i}=$ ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "-2 < k < 2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | -2 < k < 2 | [
{
"content": "When $x \\in \\mathbb{R}$, the quadratic inequality $x^2 - kx + 1 > 0$ always holds. Find the range of $k$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "97",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 97 | [
{
"content": "\nIn a $100 \\times 25$ rectangular table, each cell is filled with a non-negative real number. The number in the cell at the $i$-th row and $j$-th column is $x_{i,j}$, where $i=1, 2, \\cdots, 100$ and $j=1, 2, \\cdots, 25$. The table is represented as Table 1. The values in each column of Table 1... | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 32 | [
{
"content": "What is the maximum number of checkers that can be placed on an $8 \\times 8$ board such that each one is under attack?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_synthetic_amc | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "160",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 160 | [
{
"content": "A boy buys 4 oranges for 15 cents and sells 8 oranges for 36 cents. How many oranges must he sell to make a profit of $120$ cents?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "0 \\text{ or } 6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 0 \text{ or } 6 | [
{
"content": "Point $A$ is $3$ units away from the origin on the number line. If a point moves $4$ units to the right from point $A$ and then $1$ unit to the left, the number represented by the endpoint is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "5 - 4\\sqrt{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 5 - 4\sqrt{2} | [
{
"content": "Calculate:<br/>$(1)\\sqrt{6}\\times \\sqrt{\\frac{1}{3}}-\\sqrt{16}×\\sqrt{18}$;<br/>$(2)(2-\\sqrt{5})(2+\\sqrt{5})+(2-\\sqrt{2})^{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_olympiads | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 15 | [
{
"content": "A cooperative receives apple and grape juice in identical cans and produces apple-grape juice in identical jars. One can of apple juice is enough to make exactly 6 jars of the beverage, and one can of grape juice is enough to make exactly 10 jars. When the recipe for the beverage was changed, one ... | PRIME-Eurus-2-RL-Data |
numina_synthetic_math | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "648\\sqrt{7}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 648\sqrt{7} | [
{
"content": "A cone is formed from a 270-degree sector of a circle with a radius of 24 by aligning the two straight sides. Calculate the result when the volume of the cone is divided by $\\pi$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | PRIME-Eurus-2-RL-Data |
numina_cn_k12 | [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]... | math | {
"ground_truth": "(1), (2), (3)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (1), (2), (3) | [
{
"content": "Let $a$, $b$, $c$ represent three lines, and $\\alpha$, $\\beta$ represent two planes. Among the following propositions, identify the false statement(s): \n(1) If $c \\perp \\alpha$ and $c \\perp \\beta$, then $\\alpha \\parallel \\beta$; \n(2) If $b \\subset \\alpha$, $c \\nsubseteq \\alpha$, a... | PRIME-Eurus-2-RL-Data |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.