### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  feynau ehfpldde udledhfa trqa
### Reasoning:
<|cot_start|>Cipher text: feynau ehfpldde udledhfa trqa
Try each candidate Wonderland word against each ciphertext word:
  cipher='feynau' candidate='alice' length-match=False
  cipher='feynau' candidate='rabbit' length-match=True
  cipher='feynau' candidate='hatter' length-match=True
  cipher='feynau' candidate='cheshire' length-match=False
  cipher='feynau' candidate='queen' length-match=False
  cipher='feynau' candidate='tea' length-match=False
  cipher='feynau' candidate='cake' length-match=False
  cipher='feynau' candidate='garden' length-match=True
  cipher='feynau' candidate='mushroom' length-match=False
  cipher='feynau' candidate='card' length-match=False
  cipher='feynau' candidate='card' length-match=False
  cipher='feynau' candidate='wonderland' length-match=False
  cipher='feynau' candidate='white' length-match=False
  cipher='feynau' candidate='down' length-match=False
  cipher='feynau' candidate='smile' length-match=False
  cipher='feynau' candidate='smiled' length-match=True  <- assign
  cipher='feynau' candidate='looking' length-match=False
  cipher='feynau' candidate='glass' length-match=False
  cipher='feynau' candidate='march' length-match=False
  cipher='feynau' candidate='hare' length-match=False
  cipher='feynau' candidate='dormouse' length-match=False
  cipher='ehfpldde' candidate='alice' length-match=False
  cipher='ehfpldde' candidate='rabbit' length-match=False
  cipher='ehfpldde' candidate='hatter' length-match=False
  cipher='ehfpldde' candidate='cheshire' length-match=True
  cipher='ehfpldde' candidate='queen' length-match=False
  cipher='ehfpldde' candidate='tea' length-match=False
  cipher='ehfpldde' candidate='cake' length-match=False
  cipher='ehfpldde' candidate='garden' length-match=False
  cipher='ehfpldde' candidate='mushroom' length-match=True  <- assign
  cipher='ehfpldde' candidate='card' length-match=False
  cipher='ehfpldde' candidate='card' length-match=False
  cipher='ehfpldde' candidate='wonderland' length-match=False
  cipher='ehfpldde' candidate='white' length-match=False
  cipher='ehfpldde' candidate='down' length-match=False
  cipher='ehfpldde' candidate='smile' length-match=False
  cipher='ehfpldde' candidate='smiled' length-match=False
  cipher='ehfpldde' candidate='looking' length-match=False
  cipher='ehfpldde' candidate='glass' length-match=False
  cipher='ehfpldde' candidate='march' length-match=False
  cipher='ehfpldde' candidate='hare' length-match=False
  cipher='ehfpldde' candidate='dormouse' length-match=True
  cipher='udledhfa' candidate='alice' length-match=False
  cipher='udledhfa' candidate='rabbit' length-match=False
  cipher='udledhfa' candidate='hatter' length-match=False
  cipher='udledhfa' candidate='cheshire' length-match=True
  cipher='udledhfa' candidate='queen' length-match=False
  cipher='udledhfa' candidate='tea' length-match=False
  cipher='udledhfa' candidate='cake' length-match=False
  cipher='udledhfa' candidate='garden' length-match=False
  cipher='udledhfa' candidate='mushroom' length-match=True
  cipher='udledhfa' candidate='card' length-match=False
  cipher='udledhfa' candidate='card' length-match=False
  cipher='udledhfa' candidate='wonderland' length-match=False
  cipher='udledhfa' candidate='white' length-match=False
  cipher='udledhfa' candidate='down' length-match=False
  cipher='udledhfa' candidate='smile' length-match=False
  cipher='udledhfa' candidate='smiled' length-match=False
  cipher='udledhfa' candidate='looking' length-match=False
  cipher='udledhfa' candidate='glass' length-match=False
  cipher='udledhfa' candidate='march' length-match=False
  cipher='udledhfa' candidate='hare' length-match=False
  cipher='udledhfa' candidate='dormouse' length-match=True  <- assign
  cipher='trqa' candidate='alice' length-match=False
  cipher='trqa' candidate='rabbit' length-match=False
  cipher='trqa' candidate='hatter' length-match=False
  cipher='trqa' candidate='cheshire' length-match=False
  cipher='trqa' candidate='queen' length-match=False
  cipher='trqa' candidate='tea' length-match=False
  cipher='trqa' candidate='cake' length-match=True  <- assign
  cipher='trqa' candidate='garden' length-match=False
  cipher='trqa' candidate='mushroom' length-match=False
  cipher='trqa' candidate='card' length-match=True
  cipher='trqa' candidate='card' length-match=True
  cipher='trqa' candidate='wonderland' length-match=False
  cipher='trqa' candidate='white' length-match=False
  cipher='trqa' candidate='down' length-match=True
  cipher='trqa' candidate='smile' length-match=False
  cipher='trqa' candidate='smiled' length-match=False
  cipher='trqa' candidate='looking' length-match=False
  cipher='trqa' candidate='glass' length-match=False
  cipher='trqa' candidate='march' length-match=False
  cipher='trqa' candidate='hare' length-match=True
  cipher='trqa' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  smiled mushroom dormouse cake
Final: \boxed{smiled mushroom dormouse cake}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  68,50 -> 6850
  71,54 -> 7154
  75,38 -> 7538
Apply to: 49,82
### Reasoning:
<|cot_start|>Examples:
  68,50 -> 6850
  71,54 -> 7154
  75,38 -> 7538
Check both candidate forms:
  concat(68,50)=6850  rev_concat(68,50)=5068  target=6850  concat
  concat(71,54)=7154  rev_concat(71,54)=5471  target=7154  concat
  concat(75,38)=7538  rev_concat(75,38)=3875  target=7538  concat
Conclude operator: concat.
Apply to (49, 82):  answer = 4982
Final: \boxed{4982}


### Task: unit
### Problem:
Convert 50 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 50 kilograms = 50 * 1000 grams.
Compute step by step:
  5 * 10^1 * 1000 = 50000
  running total = 50000
  0 * 10^0 * 1000 = 0
  running total = 50000
Final: \boxed{50000}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  37,39 -> 2
  22,27 -> 5
  23,15 -> 8
Apply to: 86,81
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  37,39: '+' gives 76; target=2  no
  37,39: '-' gives 2; target=2  MATCH
  37,39: '*' gives 1443; target=2  no
  37,39: 'concat' gives 3739; target=2  no
  37,39: 'rev_concat' gives 3937; target=2  no
  37,39: 'max*min+sum' gives 1519; target=2  no
  37,39: 'digitsum2' gives 484; target=2  no
  22,27: '+' gives 49; target=5  no
  22,27: '-' gives 5; target=5  MATCH
  22,27: '*' gives 594; target=5  no
  22,27: 'concat' gives 2227; target=5  no
  22,27: 'rev_concat' gives 2722; target=5  no
  22,27: 'max*min+sum' gives 643; target=5  no
  22,27: 'digitsum2' gives 169; target=5  no
  23,15: '+' gives 38; target=8  no
  23,15: '-' gives 8; target=8  MATCH
  23,15: '*' gives 345; target=8  no
  23,15: 'concat' gives 2315; target=8  no
  23,15: 'rev_concat' gives 1523; target=8  no
  23,15: 'max*min+sum' gives 383; target=8  no
  23,15: 'digitsum2' gives 121; target=8  no
The only operator consistent with all examples is '-'.
Apply to (86, 81):
  result = 5
Final: \boxed{5}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  dsbw xzui qkrmwx xzckztqw
### Reasoning:
<|cot_start|>Cipher text: dsbw xzui qkrmwx xzckztqw
Try each candidate Wonderland word against each ciphertext word:
  cipher='dsbw' candidate='alice' length-match=False
  cipher='dsbw' candidate='rabbit' length-match=False
  cipher='dsbw' candidate='hatter' length-match=False
  cipher='dsbw' candidate='cheshire' length-match=False
  cipher='dsbw' candidate='queen' length-match=False
  cipher='dsbw' candidate='tea' length-match=False
  cipher='dsbw' candidate='cake' length-match=True  <- assign
  cipher='dsbw' candidate='garden' length-match=False
  cipher='dsbw' candidate='mushroom' length-match=False
  cipher='dsbw' candidate='card' length-match=True
  cipher='dsbw' candidate='card' length-match=True
  cipher='dsbw' candidate='wonderland' length-match=False
  cipher='dsbw' candidate='white' length-match=False
  cipher='dsbw' candidate='down' length-match=True
  cipher='dsbw' candidate='smile' length-match=False
  cipher='dsbw' candidate='smiled' length-match=False
  cipher='dsbw' candidate='looking' length-match=False
  cipher='dsbw' candidate='glass' length-match=False
  cipher='dsbw' candidate='march' length-match=False
  cipher='dsbw' candidate='hare' length-match=True
  cipher='dsbw' candidate='dormouse' length-match=False
  cipher='xzui' candidate='alice' length-match=False
  cipher='xzui' candidate='rabbit' length-match=False
  cipher='xzui' candidate='hatter' length-match=False
  cipher='xzui' candidate='cheshire' length-match=False
  cipher='xzui' candidate='queen' length-match=False
  cipher='xzui' candidate='tea' length-match=False
  cipher='xzui' candidate='cake' length-match=True
  cipher='xzui' candidate='garden' length-match=False
  cipher='xzui' candidate='mushroom' length-match=False
  cipher='xzui' candidate='card' length-match=True
  cipher='xzui' candidate='card' length-match=True
  cipher='xzui' candidate='wonderland' length-match=False
  cipher='xzui' candidate='white' length-match=False
  cipher='xzui' candidate='down' length-match=True  <- assign
  cipher='xzui' candidate='smile' length-match=False
  cipher='xzui' candidate='smiled' length-match=False
  cipher='xzui' candidate='looking' length-match=False
  cipher='xzui' candidate='glass' length-match=False
  cipher='xzui' candidate='march' length-match=False
  cipher='xzui' candidate='hare' length-match=True
  cipher='xzui' candidate='dormouse' length-match=False
  cipher='qkrmwx' candidate='alice' length-match=False
  cipher='qkrmwx' candidate='rabbit' length-match=True
  cipher='qkrmwx' candidate='hatter' length-match=True
  cipher='qkrmwx' candidate='cheshire' length-match=False
  cipher='qkrmwx' candidate='queen' length-match=False
  cipher='qkrmwx' candidate='tea' length-match=False
  cipher='qkrmwx' candidate='cake' length-match=False
  cipher='qkrmwx' candidate='garden' length-match=True
  cipher='qkrmwx' candidate='mushroom' length-match=False
  cipher='qkrmwx' candidate='card' length-match=False
  cipher='qkrmwx' candidate='card' length-match=False
  cipher='qkrmwx' candidate='wonderland' length-match=False
  cipher='qkrmwx' candidate='white' length-match=False
  cipher='qkrmwx' candidate='down' length-match=False
  cipher='qkrmwx' candidate='smile' length-match=False
  cipher='qkrmwx' candidate='smiled' length-match=True  <- assign
  cipher='qkrmwx' candidate='looking' length-match=False
  cipher='qkrmwx' candidate='glass' length-match=False
  cipher='qkrmwx' candidate='march' length-match=False
  cipher='qkrmwx' candidate='hare' length-match=False
  cipher='qkrmwx' candidate='dormouse' length-match=False
  cipher='xzckztqw' candidate='alice' length-match=False
  cipher='xzckztqw' candidate='rabbit' length-match=False
  cipher='xzckztqw' candidate='hatter' length-match=False
  cipher='xzckztqw' candidate='cheshire' length-match=True
  cipher='xzckztqw' candidate='queen' length-match=False
  cipher='xzckztqw' candidate='tea' length-match=False
  cipher='xzckztqw' candidate='cake' length-match=False
  cipher='xzckztqw' candidate='garden' length-match=False
  cipher='xzckztqw' candidate='mushroom' length-match=True
  cipher='xzckztqw' candidate='card' length-match=False
  cipher='xzckztqw' candidate='card' length-match=False
  cipher='xzckztqw' candidate='wonderland' length-match=False
  cipher='xzckztqw' candidate='white' length-match=False
  cipher='xzckztqw' candidate='down' length-match=False
  cipher='xzckztqw' candidate='smile' length-match=False
  cipher='xzckztqw' candidate='smiled' length-match=False
  cipher='xzckztqw' candidate='looking' length-match=False
  cipher='xzckztqw' candidate='glass' length-match=False
  cipher='xzckztqw' candidate='march' length-match=False
  cipher='xzckztqw' candidate='hare' length-match=False
  cipher='xzckztqw' candidate='dormouse' length-match=True  <- assign
Assemble the decoded sentence:
  cake down smiled dormouse
Final: \boxed{cake down smiled dormouse}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10001100 -> 11011001
  11000110 -> 10010011
  10110110 -> 11100011
Apply to: 00010000
### Reasoning:
<|cot_start|>Given examples:
  10001100 -> 11011001
  11000110 -> 10010011
  10110110 -> 11100011
Compare each bit position across the three examples:
  bit 0: 1,1,1 -> 1,1,1
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 0,0,1 -> 0,0,1
  bit 3: 0,0,1 -> 1,1,0
  bit 4: 1,0,0 -> 1,0,0
  bit 5: 1,1,1 -> 0,0,0
  bit 6: 0,1,1 -> 0,1,1
  bit 7: 0,0,0 -> 1,1,1
Deduce rule: xor 0x55.
Apply to 00010000:
  result = 01000101
Final: \boxed{01000101}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  67,30 -> 6730
  83,59 -> 8359
  39,26 -> 3926
Apply to: 42,12
### Reasoning:
<|cot_start|>Examples:
  67,30 -> 6730
  83,59 -> 8359
  39,26 -> 3926
Check both candidate forms:
  concat(67,30)=6730  rev_concat(67,30)=3067  target=6730  concat
  concat(83,59)=8359  rev_concat(83,59)=5983  target=8359  concat
  concat(39,26)=3926  rev_concat(39,26)=2639  target=3926  concat
Conclude operator: concat.
Apply to (42, 12):  answer = 4212
Final: \boxed{4212}


### Task: gravity
### Problem:
A mass of 42 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 42 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  2 * 10^0 * 981 = 1962
  running total = 41202
So F = 41202 centiNewtons = 412.02 N.
Final: \boxed{412.02}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10010011 -> 11110011
  00011111 -> 11111111
  01111101 -> 11111101
Apply to: 00111000
### Reasoning:
<|cot_start|>Given examples:
  10010011 -> 11110011
  00011111 -> 11111111
  01111101 -> 11111101
Compare each bit position across the three examples:
  bit 0: 1,0,0 -> 1,1,1
  bit 1: 0,0,1 -> 1,1,1
  bit 2: 0,0,1 -> 1,1,1
  bit 3: 1,1,1 -> 1,1,1
  bit 4: 0,1,1 -> 0,1,1
  bit 5: 0,1,1 -> 0,1,1
  bit 6: 1,1,0 -> 1,1,0
  bit 7: 1,1,1 -> 1,1,1
Deduce rule: or 0xF0.
Apply to 00111000:
  result = 11111000
Final: \boxed{11111000}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  vrucc owmcwqbm help hebfegcm
### Reasoning:
<|cot_start|>Cipher text: vrucc owmcwqbm help hebfegcm
Try each candidate Wonderland word against each ciphertext word:
  cipher='vrucc' candidate='alice' length-match=True
  cipher='vrucc' candidate='rabbit' length-match=False
  cipher='vrucc' candidate='hatter' length-match=False
  cipher='vrucc' candidate='cheshire' length-match=False
  cipher='vrucc' candidate='queen' length-match=True
  cipher='vrucc' candidate='tea' length-match=False
  cipher='vrucc' candidate='cake' length-match=False
  cipher='vrucc' candidate='garden' length-match=False
  cipher='vrucc' candidate='mushroom' length-match=False
  cipher='vrucc' candidate='card' length-match=False
  cipher='vrucc' candidate='card' length-match=False
  cipher='vrucc' candidate='wonderland' length-match=False
  cipher='vrucc' candidate='white' length-match=True
  cipher='vrucc' candidate='down' length-match=False
  cipher='vrucc' candidate='smile' length-match=True
  cipher='vrucc' candidate='smiled' length-match=False
  cipher='vrucc' candidate='looking' length-match=False
  cipher='vrucc' candidate='glass' length-match=True  <- assign
  cipher='vrucc' candidate='march' length-match=True
  cipher='vrucc' candidate='hare' length-match=False
  cipher='vrucc' candidate='dormouse' length-match=False
  cipher='owmcwqbm' candidate='alice' length-match=False
  cipher='owmcwqbm' candidate='rabbit' length-match=False
  cipher='owmcwqbm' candidate='hatter' length-match=False
  cipher='owmcwqbm' candidate='cheshire' length-match=True  <- assign
  cipher='owmcwqbm' candidate='queen' length-match=False
  cipher='owmcwqbm' candidate='tea' length-match=False
  cipher='owmcwqbm' candidate='cake' length-match=False
  cipher='owmcwqbm' candidate='garden' length-match=False
  cipher='owmcwqbm' candidate='mushroom' length-match=True
  cipher='owmcwqbm' candidate='card' length-match=False
  cipher='owmcwqbm' candidate='card' length-match=False
  cipher='owmcwqbm' candidate='wonderland' length-match=False
  cipher='owmcwqbm' candidate='white' length-match=False
  cipher='owmcwqbm' candidate='down' length-match=False
  cipher='owmcwqbm' candidate='smile' length-match=False
  cipher='owmcwqbm' candidate='smiled' length-match=False
  cipher='owmcwqbm' candidate='looking' length-match=False
  cipher='owmcwqbm' candidate='glass' length-match=False
  cipher='owmcwqbm' candidate='march' length-match=False
  cipher='owmcwqbm' candidate='hare' length-match=False
  cipher='owmcwqbm' candidate='dormouse' length-match=True
  cipher='help' candidate='alice' length-match=False
  cipher='help' candidate='rabbit' length-match=False
  cipher='help' candidate='hatter' length-match=False
  cipher='help' candidate='cheshire' length-match=False
  cipher='help' candidate='queen' length-match=False
  cipher='help' candidate='tea' length-match=False
  cipher='help' candidate='cake' length-match=True
  cipher='help' candidate='garden' length-match=False
  cipher='help' candidate='mushroom' length-match=False
  cipher='help' candidate='card' length-match=True
  cipher='help' candidate='card' length-match=True
  cipher='help' candidate='wonderland' length-match=False
  cipher='help' candidate='white' length-match=False
  cipher='help' candidate='down' length-match=True  <- assign
  cipher='help' candidate='smile' length-match=False
  cipher='help' candidate='smiled' length-match=False
  cipher='help' candidate='looking' length-match=False
  cipher='help' candidate='glass' length-match=False
  cipher='help' candidate='march' length-match=False
  cipher='help' candidate='hare' length-match=True
  cipher='help' candidate='dormouse' length-match=False
  cipher='hebfegcm' candidate='alice' length-match=False
  cipher='hebfegcm' candidate='rabbit' length-match=False
  cipher='hebfegcm' candidate='hatter' length-match=False
  cipher='hebfegcm' candidate='cheshire' length-match=True
  cipher='hebfegcm' candidate='queen' length-match=False
  cipher='hebfegcm' candidate='tea' length-match=False
  cipher='hebfegcm' candidate='cake' length-match=False
  cipher='hebfegcm' candidate='garden' length-match=False
  cipher='hebfegcm' candidate='mushroom' length-match=True
  cipher='hebfegcm' candidate='card' length-match=False
  cipher='hebfegcm' candidate='card' length-match=False
  cipher='hebfegcm' candidate='wonderland' length-match=False
  cipher='hebfegcm' candidate='white' length-match=False
  cipher='hebfegcm' candidate='down' length-match=False
  cipher='hebfegcm' candidate='smile' length-match=False
  cipher='hebfegcm' candidate='smiled' length-match=False
  cipher='hebfegcm' candidate='looking' length-match=False
  cipher='hebfegcm' candidate='glass' length-match=False
  cipher='hebfegcm' candidate='march' length-match=False
  cipher='hebfegcm' candidate='hare' length-match=False
  cipher='hebfegcm' candidate='dormouse' length-match=True  <- assign
Assemble the decoded sentence:
  glass cheshire down dormouse
Final: \boxed{glass cheshire down dormouse}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  jczbclyg ybvogj pngynvzg uovpg
### Reasoning:
<|cot_start|>Cipher text: jczbclyg ybvogj pngynvzg uovpg
Try each candidate Wonderland word against each ciphertext word:
  cipher='jczbclyg' candidate='alice' length-match=False
  cipher='jczbclyg' candidate='rabbit' length-match=False
  cipher='jczbclyg' candidate='hatter' length-match=False
  cipher='jczbclyg' candidate='cheshire' length-match=True
  cipher='jczbclyg' candidate='queen' length-match=False
  cipher='jczbclyg' candidate='tea' length-match=False
  cipher='jczbclyg' candidate='cake' length-match=False
  cipher='jczbclyg' candidate='garden' length-match=False
  cipher='jczbclyg' candidate='mushroom' length-match=True
  cipher='jczbclyg' candidate='card' length-match=False
  cipher='jczbclyg' candidate='card' length-match=False
  cipher='jczbclyg' candidate='wonderland' length-match=False
  cipher='jczbclyg' candidate='white' length-match=False
  cipher='jczbclyg' candidate='down' length-match=False
  cipher='jczbclyg' candidate='smile' length-match=False
  cipher='jczbclyg' candidate='smiled' length-match=False
  cipher='jczbclyg' candidate='looking' length-match=False
  cipher='jczbclyg' candidate='glass' length-match=False
  cipher='jczbclyg' candidate='march' length-match=False
  cipher='jczbclyg' candidate='hare' length-match=False
  cipher='jczbclyg' candidate='dormouse' length-match=True  <- assign
  cipher='ybvogj' candidate='alice' length-match=False
  cipher='ybvogj' candidate='rabbit' length-match=True
  cipher='ybvogj' candidate='hatter' length-match=True
  cipher='ybvogj' candidate='cheshire' length-match=False
  cipher='ybvogj' candidate='queen' length-match=False
  cipher='ybvogj' candidate='tea' length-match=False
  cipher='ybvogj' candidate='cake' length-match=False
  cipher='ybvogj' candidate='garden' length-match=True
  cipher='ybvogj' candidate='mushroom' length-match=False
  cipher='ybvogj' candidate='card' length-match=False
  cipher='ybvogj' candidate='card' length-match=False
  cipher='ybvogj' candidate='wonderland' length-match=False
  cipher='ybvogj' candidate='white' length-match=False
  cipher='ybvogj' candidate='down' length-match=False
  cipher='ybvogj' candidate='smile' length-match=False
  cipher='ybvogj' candidate='smiled' length-match=True  <- assign
  cipher='ybvogj' candidate='looking' length-match=False
  cipher='ybvogj' candidate='glass' length-match=False
  cipher='ybvogj' candidate='march' length-match=False
  cipher='ybvogj' candidate='hare' length-match=False
  cipher='ybvogj' candidate='dormouse' length-match=False
  cipher='pngynvzg' candidate='alice' length-match=False
  cipher='pngynvzg' candidate='rabbit' length-match=False
  cipher='pngynvzg' candidate='hatter' length-match=False
  cipher='pngynvzg' candidate='cheshire' length-match=True  <- assign
  cipher='pngynvzg' candidate='queen' length-match=False
  cipher='pngynvzg' candidate='tea' length-match=False
  cipher='pngynvzg' candidate='cake' length-match=False
  cipher='pngynvzg' candidate='garden' length-match=False
  cipher='pngynvzg' candidate='mushroom' length-match=True
  cipher='pngynvzg' candidate='card' length-match=False
  cipher='pngynvzg' candidate='card' length-match=False
  cipher='pngynvzg' candidate='wonderland' length-match=False
  cipher='pngynvzg' candidate='white' length-match=False
  cipher='pngynvzg' candidate='down' length-match=False
  cipher='pngynvzg' candidate='smile' length-match=False
  cipher='pngynvzg' candidate='smiled' length-match=False
  cipher='pngynvzg' candidate='looking' length-match=False
  cipher='pngynvzg' candidate='glass' length-match=False
  cipher='pngynvzg' candidate='march' length-match=False
  cipher='pngynvzg' candidate='hare' length-match=False
  cipher='pngynvzg' candidate='dormouse' length-match=True
  cipher='uovpg' candidate='alice' length-match=True  <- assign
  cipher='uovpg' candidate='rabbit' length-match=False
  cipher='uovpg' candidate='hatter' length-match=False
  cipher='uovpg' candidate='cheshire' length-match=False
  cipher='uovpg' candidate='queen' length-match=True
  cipher='uovpg' candidate='tea' length-match=False
  cipher='uovpg' candidate='cake' length-match=False
  cipher='uovpg' candidate='garden' length-match=False
  cipher='uovpg' candidate='mushroom' length-match=False
  cipher='uovpg' candidate='card' length-match=False
  cipher='uovpg' candidate='card' length-match=False
  cipher='uovpg' candidate='wonderland' length-match=False
  cipher='uovpg' candidate='white' length-match=True
  cipher='uovpg' candidate='down' length-match=False
  cipher='uovpg' candidate='smile' length-match=True
  cipher='uovpg' candidate='smiled' length-match=False
  cipher='uovpg' candidate='looking' length-match=False
  cipher='uovpg' candidate='glass' length-match=True
  cipher='uovpg' candidate='march' length-match=True
  cipher='uovpg' candidate='hare' length-match=False
  cipher='uovpg' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  dormouse smiled cheshire alice
Final: \boxed{dormouse smiled cheshire alice}


### Task: numeral
### Problem:
Convert the Roman numeral XII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  I = 1  ->  10 + 1 = 11
  I = 1  ->  11 + 1 = 12
Final: \boxed{12}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  83,87 -> 8783
  86,47 -> 4786
  23,53 -> 5323
Apply to: 98,21
### Reasoning:
<|cot_start|>Examples:
  83,87 -> 8783
  86,47 -> 4786
  23,53 -> 5323
Check both candidate forms:
  concat(83,87)=8387  rev_concat(83,87)=8783  target=8783  rev_concat
  concat(86,47)=8647  rev_concat(86,47)=4786  target=4786  rev_concat
  concat(23,53)=2353  rev_concat(23,53)=5323  target=5323  rev_concat
Conclude operator: rev_concat.
Apply to (98, 21):  answer = 2198
Final: \boxed{2198}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  79,14 -> 7914
  37,85 -> 3785
  84,62 -> 8462
Apply to: 45,22
### Reasoning:
<|cot_start|>Examples:
  79,14 -> 7914
  37,85 -> 3785
  84,62 -> 8462
Check both candidate forms:
  concat(79,14)=7914  rev_concat(79,14)=1479  target=7914  concat
  concat(37,85)=3785  rev_concat(37,85)=8537  target=3785  concat
  concat(84,62)=8462  rev_concat(84,62)=6284  target=8462  concat
Conclude operator: concat.
Apply to (45, 22):  answer = 4522
Final: \boxed{4522}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  evo agruvnsoru zonhl loeevn
### Reasoning:
<|cot_start|>Cipher text: evo agruvnsoru zonhl loeevn
Try each candidate Wonderland word against each ciphertext word:
  cipher='evo' candidate='alice' length-match=False
  cipher='evo' candidate='rabbit' length-match=False
  cipher='evo' candidate='hatter' length-match=False
  cipher='evo' candidate='cheshire' length-match=False
  cipher='evo' candidate='queen' length-match=False
  cipher='evo' candidate='tea' length-match=True  <- assign
  cipher='evo' candidate='cake' length-match=False
  cipher='evo' candidate='garden' length-match=False
  cipher='evo' candidate='mushroom' length-match=False
  cipher='evo' candidate='card' length-match=False
  cipher='evo' candidate='card' length-match=False
  cipher='evo' candidate='wonderland' length-match=False
  cipher='evo' candidate='white' length-match=False
  cipher='evo' candidate='down' length-match=False
  cipher='evo' candidate='smile' length-match=False
  cipher='evo' candidate='smiled' length-match=False
  cipher='evo' candidate='looking' length-match=False
  cipher='evo' candidate='glass' length-match=False
  cipher='evo' candidate='march' length-match=False
  cipher='evo' candidate='hare' length-match=False
  cipher='evo' candidate='dormouse' length-match=False
  cipher='agruvnsoru' candidate='alice' length-match=False
  cipher='agruvnsoru' candidate='rabbit' length-match=False
  cipher='agruvnsoru' candidate='hatter' length-match=False
  cipher='agruvnsoru' candidate='cheshire' length-match=False
  cipher='agruvnsoru' candidate='queen' length-match=False
  cipher='agruvnsoru' candidate='tea' length-match=False
  cipher='agruvnsoru' candidate='cake' length-match=False
  cipher='agruvnsoru' candidate='garden' length-match=False
  cipher='agruvnsoru' candidate='mushroom' length-match=False
  cipher='agruvnsoru' candidate='card' length-match=False
  cipher='agruvnsoru' candidate='card' length-match=False
  cipher='agruvnsoru' candidate='wonderland' length-match=True  <- assign
  cipher='agruvnsoru' candidate='white' length-match=False
  cipher='agruvnsoru' candidate='down' length-match=False
  cipher='agruvnsoru' candidate='smile' length-match=False
  cipher='agruvnsoru' candidate='smiled' length-match=False
  cipher='agruvnsoru' candidate='looking' length-match=False
  cipher='agruvnsoru' candidate='glass' length-match=False
  cipher='agruvnsoru' candidate='march' length-match=False
  cipher='agruvnsoru' candidate='hare' length-match=False
  cipher='agruvnsoru' candidate='dormouse' length-match=False
  cipher='zonhl' candidate='alice' length-match=True
  cipher='zonhl' candidate='rabbit' length-match=False
  cipher='zonhl' candidate='hatter' length-match=False
  cipher='zonhl' candidate='cheshire' length-match=False
  cipher='zonhl' candidate='queen' length-match=True
  cipher='zonhl' candidate='tea' length-match=False
  cipher='zonhl' candidate='cake' length-match=False
  cipher='zonhl' candidate='garden' length-match=False
  cipher='zonhl' candidate='mushroom' length-match=False
  cipher='zonhl' candidate='card' length-match=False
  cipher='zonhl' candidate='card' length-match=False
  cipher='zonhl' candidate='wonderland' length-match=False
  cipher='zonhl' candidate='white' length-match=True
  cipher='zonhl' candidate='down' length-match=False
  cipher='zonhl' candidate='smile' length-match=True
  cipher='zonhl' candidate='smiled' length-match=False
  cipher='zonhl' candidate='looking' length-match=False
  cipher='zonhl' candidate='glass' length-match=True
  cipher='zonhl' candidate='march' length-match=True  <- assign
  cipher='zonhl' candidate='hare' length-match=False
  cipher='zonhl' candidate='dormouse' length-match=False
  cipher='loeevn' candidate='alice' length-match=False
  cipher='loeevn' candidate='rabbit' length-match=True
  cipher='loeevn' candidate='hatter' length-match=True  <- assign
  cipher='loeevn' candidate='cheshire' length-match=False
  cipher='loeevn' candidate='queen' length-match=False
  cipher='loeevn' candidate='tea' length-match=False
  cipher='loeevn' candidate='cake' length-match=False
  cipher='loeevn' candidate='garden' length-match=True
  cipher='loeevn' candidate='mushroom' length-match=False
  cipher='loeevn' candidate='card' length-match=False
  cipher='loeevn' candidate='card' length-match=False
  cipher='loeevn' candidate='wonderland' length-match=False
  cipher='loeevn' candidate='white' length-match=False
  cipher='loeevn' candidate='down' length-match=False
  cipher='loeevn' candidate='smile' length-match=False
  cipher='loeevn' candidate='smiled' length-match=True
  cipher='loeevn' candidate='looking' length-match=False
  cipher='loeevn' candidate='glass' length-match=False
  cipher='loeevn' candidate='march' length-match=False
  cipher='loeevn' candidate='hare' length-match=False
  cipher='loeevn' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  tea wonderland march hatter
Final: \boxed{tea wonderland march hatter}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  31,54 -> 1759
  60,13 -> 853
  78,95 -> 7583
Apply to: 15,78
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  31,54: '+' gives 85; target=1759  no
  31,54: '-' gives 23; target=1759  no
  31,54: '*' gives 1674; target=1759  no
  31,54: 'concat' gives 3154; target=1759  no
  31,54: 'rev_concat' gives 5431; target=1759  no
  31,54: 'max*min+sum' gives 1759; target=1759  MATCH
  31,54: 'digitsum2' gives 169; target=1759  no
  60,13: '+' gives 73; target=853  no
  60,13: '-' gives 47; target=853  no
  60,13: '*' gives 780; target=853  no
  60,13: 'concat' gives 6013; target=853  no
  60,13: 'rev_concat' gives 1360; target=853  no
  60,13: 'max*min+sum' gives 853; target=853  MATCH
  60,13: 'digitsum2' gives 100; target=853  no
  78,95: '+' gives 173; target=7583  no
  78,95: '-' gives 17; target=7583  no
  78,95: '*' gives 7410; target=7583  no
  78,95: 'concat' gives 7895; target=7583  no
  78,95: 'rev_concat' gives 9578; target=7583  no
  78,95: 'max*min+sum' gives 7583; target=7583  MATCH
  78,95: 'digitsum2' gives 841; target=7583  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (15, 78):
  result = 1263
Final: \boxed{1263}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  53,79 -> 4319
  22,21 -> 505
  60,11 -> 731
Apply to: 17,34
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  53,79: '+' gives 132; target=4319  no
  53,79: '-' gives 26; target=4319  no
  53,79: '*' gives 4187; target=4319  no
  53,79: 'concat' gives 5379; target=4319  no
  53,79: 'rev_concat' gives 7953; target=4319  no
  53,79: 'max*min+sum' gives 4319; target=4319  MATCH
  53,79: 'digitsum2' gives 576; target=4319  no
  22,21: '+' gives 43; target=505  no
  22,21: '-' gives 1; target=505  no
  22,21: '*' gives 462; target=505  no
  22,21: 'concat' gives 2221; target=505  no
  22,21: 'rev_concat' gives 2122; target=505  no
  22,21: 'max*min+sum' gives 505; target=505  MATCH
  22,21: 'digitsum2' gives 49; target=505  no
  60,11: '+' gives 71; target=731  no
  60,11: '-' gives 49; target=731  no
  60,11: '*' gives 660; target=731  no
  60,11: 'concat' gives 6011; target=731  no
  60,11: 'rev_concat' gives 1160; target=731  no
  60,11: 'max*min+sum' gives 731; target=731  MATCH
  60,11: 'digitsum2' gives 64; target=731  no
The only operator consistent with all examples is 'max*min+sum'.
Apply to (17, 34):
  result = 629
Final: \boxed{629}


### Task: gravity
### Problem:
A mass of 46 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 46 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  6 * 10^0 * 981 = 5886
  running total = 45126
So F = 45126 centiNewtons = 451.26 N.
Final: \boxed{451.26}


### Task: numeral
### Problem:
Convert the Roman numeral LXXXII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  X = 10  ->  60 + 10 = 70
  X = 10  ->  70 + 10 = 80
  I = 1  ->  80 + 1 = 81
  I = 1  ->  81 + 1 = 82
Final: \boxed{82}


### Task: unit
### Problem:
Convert 17 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 17 days = 17 * 24 hours.
Compute step by step:
  1 * 10^1 * 24 = 240
  running total = 240
  7 * 10^0 * 24 = 168
  running total = 408
Final: \boxed{408}


### Task: unit
### Problem:
Convert 28 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 28 days = 28 * 24 hours.
Compute step by step:
  2 * 10^1 * 24 = 480
  running total = 480
  8 * 10^0 * 24 = 192
  running total = 672
Final: \boxed{672}


### Task: unit
### Problem:
Convert 16 kilograms to grams.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilograms = 1000 grams.
So 16 kilograms = 16 * 1000 grams.
Compute step by step:
  1 * 10^1 * 1000 = 10000
  running total = 10000
  6 * 10^0 * 1000 = 6000
  running total = 16000
Final: \boxed{16000}


### Task: gravity
### Problem:
A mass of 1 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 1 * 981.
Step-by-step multiplication:
  1 * 10^0 * 981 = 981
  running total = 981
So F = 981 centiNewtons = 9.81 N.
Final: \boxed{9.81}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  58,35 -> 2030
  12,60 -> 720
  90,84 -> 7560
Apply to: 78,49
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  58,35: '+' gives 93; target=2030  no
  58,35: '-' gives 23; target=2030  no
  58,35: '*' gives 2030; target=2030  MATCH
  58,35: 'concat' gives 5835; target=2030  no
  58,35: 'rev_concat' gives 3558; target=2030  no
  58,35: 'max*min+sum' gives 2123; target=2030  no
  58,35: 'digitsum2' gives 441; target=2030  no
  12,60: '+' gives 72; target=720  no
  12,60: '-' gives 48; target=720  no
  12,60: '*' gives 720; target=720  MATCH
  12,60: 'concat' gives 1260; target=720  no
  12,60: 'rev_concat' gives 6012; target=720  no
  12,60: 'max*min+sum' gives 792; target=720  no
  12,60: 'digitsum2' gives 81; target=720  no
  90,84: '+' gives 174; target=7560  no
  90,84: '-' gives 6; target=7560  no
  90,84: '*' gives 7560; target=7560  MATCH
  90,84: 'concat' gives 9084; target=7560  no
  90,84: 'rev_concat' gives 8490; target=7560  no
  90,84: 'max*min+sum' gives 7734; target=7560  no
  90,84: 'digitsum2' gives 441; target=7560  no
The only operator consistent with all examples is '*'.
Apply to (78, 49):
  result = 3822
Final: \boxed{3822}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  74,24 -> 7424
  50,84 -> 5084
  84,81 -> 8481
Apply to: 90,89
### Reasoning:
<|cot_start|>Examples:
  74,24 -> 7424
  50,84 -> 5084
  84,81 -> 8481
Check both candidate forms:
  concat(74,24)=7424  rev_concat(74,24)=2474  target=7424  concat
  concat(50,84)=5084  rev_concat(50,84)=8450  target=5084  concat
  concat(84,81)=8481  rev_concat(84,81)=8184  target=8481  concat
Conclude operator: concat.
Apply to (90, 89):  answer = 9089
Final: \boxed{9089}


### Task: unit
### Problem:
Convert 15 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 15 days = 15 * 24 hours.
Compute step by step:
  1 * 10^1 * 24 = 240
  running total = 240
  5 * 10^0 * 24 = 120
  running total = 360
Final: \boxed{360}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  94,28 -> 9428
  28,17 -> 2817
  24,29 -> 2429
Apply to: 90,25
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  94,28: '+' gives 122; target=9428  no
  94,28: '-' gives 66; target=9428  no
  94,28: '*' gives 2632; target=9428  no
  94,28: 'concat' gives 9428; target=9428  MATCH
  94,28: 'rev_concat' gives 2894; target=9428  no
  94,28: 'max*min+sum' gives 2754; target=9428  no
  94,28: 'digitsum2' gives 529; target=9428  no
  28,17: '+' gives 45; target=2817  no
  28,17: '-' gives 11; target=2817  no
  28,17: '*' gives 476; target=2817  no
  28,17: 'concat' gives 2817; target=2817  MATCH
  28,17: 'rev_concat' gives 1728; target=2817  no
  28,17: 'max*min+sum' gives 521; target=2817  no
  28,17: 'digitsum2' gives 324; target=2817  no
  24,29: '+' gives 53; target=2429  no
  24,29: '-' gives 5; target=2429  no
  24,29: '*' gives 696; target=2429  no
  24,29: 'concat' gives 2429; target=2429  MATCH
  24,29: 'rev_concat' gives 2924; target=2429  no
  24,29: 'max*min+sum' gives 749; target=2429  no
  24,29: 'digitsum2' gives 289; target=2429  no
The only operator consistent with all examples is 'concat'.
Apply to (90, 25):
  result = 9025
Final: \boxed{9025}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  71,34 -> 37
  31,89 -> 58
  34,19 -> 15
Apply to: 44,74
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  71,34: '+' gives 105; target=37  no
  71,34: '-' gives 37; target=37  MATCH
  71,34: '*' gives 2414; target=37  no
  71,34: 'concat' gives 7134; target=37  no
  71,34: 'rev_concat' gives 3471; target=37  no
  71,34: 'max*min+sum' gives 2519; target=37  no
  71,34: 'digitsum2' gives 225; target=37  no
  31,89: '+' gives 120; target=58  no
  31,89: '-' gives 58; target=58  MATCH
  31,89: '*' gives 2759; target=58  no
  31,89: 'concat' gives 3189; target=58  no
  31,89: 'rev_concat' gives 8931; target=58  no
  31,89: 'max*min+sum' gives 2879; target=58  no
  31,89: 'digitsum2' gives 441; target=58  no
  34,19: '+' gives 53; target=15  no
  34,19: '-' gives 15; target=15  MATCH
  34,19: '*' gives 646; target=15  no
  34,19: 'concat' gives 3419; target=15  no
  34,19: 'rev_concat' gives 1934; target=15  no
  34,19: 'max*min+sum' gives 699; target=15  no
  34,19: 'digitsum2' gives 289; target=15  no
The only operator consistent with all examples is '-'.
Apply to (44, 74):
  result = 30
Final: \boxed{30}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  82,79 -> 7982
  94,58 -> 5894
  63,50 -> 5063
Apply to: 87,53
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  82,79: '+' gives 161; target=7982  no
  82,79: '-' gives 3; target=7982  no
  82,79: '*' gives 6478; target=7982  no
  82,79: 'concat' gives 8279; target=7982  no
  82,79: 'rev_concat' gives 7982; target=7982  MATCH
  82,79: 'max*min+sum' gives 6639; target=7982  no
  82,79: 'digitsum2' gives 676; target=7982  no
  94,58: '+' gives 152; target=5894  no
  94,58: '-' gives 36; target=5894  no
  94,58: '*' gives 5452; target=5894  no
  94,58: 'concat' gives 9458; target=5894  no
  94,58: 'rev_concat' gives 5894; target=5894  MATCH
  94,58: 'max*min+sum' gives 5604; target=5894  no
  94,58: 'digitsum2' gives 676; target=5894  no
  63,50: '+' gives 113; target=5063  no
  63,50: '-' gives 13; target=5063  no
  63,50: '*' gives 3150; target=5063  no
  63,50: 'concat' gives 6350; target=5063  no
  63,50: 'rev_concat' gives 5063; target=5063  MATCH
  63,50: 'max*min+sum' gives 3263; target=5063  no
  63,50: 'digitsum2' gives 196; target=5063  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (87, 53):
  result = 5387
Final: \boxed{5387}


### Task: numeral
### Problem:
Convert the Roman numeral LXXII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  X = 10  ->  60 + 10 = 70
  I = 1  ->  70 + 1 = 71
  I = 1  ->  71 + 1 = 72
Final: \boxed{72}


### Task: numeral
### Problem:
Convert the Roman numeral XCIV to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  IV = 4  ->  90 + 4 = 94
Final: \boxed{94}


### Task: unit
### Problem:
Convert 98 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 98 metres = 98 * 100 centimetres.
Compute step by step:
  9 * 10^1 * 100 = 9000
  running total = 9000
  8 * 10^0 * 100 = 800
  running total = 9800
Final: \boxed{9800}


### Task: unit
### Problem:
Convert 88 minutes to seconds.
### Reasoning:
<|cot_start|>Conversion factor: 1 minutes = 60 seconds.
So 88 minutes = 88 * 60 seconds.
Compute step by step:
  8 * 10^1 * 60 = 4800
  running total = 4800
  8 * 10^0 * 60 = 480
  running total = 5280
Final: \boxed{5280}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01000010 -> 11110010
  10101001 -> 11111001
  11000110 -> 11110110
Apply to: 01100110
### Reasoning:
<|cot_start|>Given examples:
  01000010 -> 11110010
  10101001 -> 11111001
  11000110 -> 11110110
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 1,1,1
  bit 1: 1,0,1 -> 1,1,1
  bit 2: 0,1,0 -> 1,1,1
  bit 3: 0,0,0 -> 1,1,1
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 0,0,1 -> 0,0,1
  bit 6: 1,0,1 -> 1,0,1
  bit 7: 0,1,0 -> 0,1,0
Deduce rule: or 0xF0.
Apply to 01100110:
  result = 11110110
Final: \boxed{11110110}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  14,11 -> 154
  92,86 -> 7912
  61,11 -> 671
Apply to: 65,39
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  14,11: '+' gives 25; target=154  no
  14,11: '-' gives 3; target=154  no
  14,11: '*' gives 154; target=154  MATCH
  14,11: 'concat' gives 1411; target=154  no
  14,11: 'rev_concat' gives 1114; target=154  no
  14,11: 'max*min+sum' gives 179; target=154  no
  14,11: 'digitsum2' gives 49; target=154  no
  92,86: '+' gives 178; target=7912  no
  92,86: '-' gives 6; target=7912  no
  92,86: '*' gives 7912; target=7912  MATCH
  92,86: 'concat' gives 9286; target=7912  no
  92,86: 'rev_concat' gives 8692; target=7912  no
  92,86: 'max*min+sum' gives 8090; target=7912  no
  92,86: 'digitsum2' gives 625; target=7912  no
  61,11: '+' gives 72; target=671  no
  61,11: '-' gives 50; target=671  no
  61,11: '*' gives 671; target=671  MATCH
  61,11: 'concat' gives 6111; target=671  no
  61,11: 'rev_concat' gives 1161; target=671  no
  61,11: 'max*min+sum' gives 743; target=671  no
  61,11: 'digitsum2' gives 81; target=671  no
The only operator consistent with all examples is '*'.
Apply to (65, 39):
  result = 2535
Final: \boxed{2535}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  74,27 -> 47
  28,18 -> 10
  53,34 -> 19
Apply to: 15,13
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  74,27: '+' gives 101; target=47  no
  74,27: '-' gives 47; target=47  MATCH
  74,27: '*' gives 1998; target=47  no
  74,27: 'concat' gives 7427; target=47  no
  74,27: 'rev_concat' gives 2774; target=47  no
  74,27: 'max*min+sum' gives 2099; target=47  no
  74,27: 'digitsum2' gives 400; target=47  no
  28,18: '+' gives 46; target=10  no
  28,18: '-' gives 10; target=10  MATCH
  28,18: '*' gives 504; target=10  no
  28,18: 'concat' gives 2818; target=10  no
  28,18: 'rev_concat' gives 1828; target=10  no
  28,18: 'max*min+sum' gives 550; target=10  no
  28,18: 'digitsum2' gives 361; target=10  no
  53,34: '+' gives 87; target=19  no
  53,34: '-' gives 19; target=19  MATCH
  53,34: '*' gives 1802; target=19  no
  53,34: 'concat' gives 5334; target=19  no
  53,34: 'rev_concat' gives 3453; target=19  no
  53,34: 'max*min+sum' gives 1889; target=19  no
  53,34: 'digitsum2' gives 225; target=19  no
The only operator consistent with all examples is '-'.
Apply to (15, 13):
  result = 2
Final: \boxed{2}


### Task: numeral
### Problem:
Convert the Roman numeral XLII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XL = 40  ->  0 + 40 = 40
  I = 1  ->  40 + 1 = 41
  I = 1  ->  41 + 1 = 42
Final: \boxed{42}


### Task: gravity
### Problem:
A mass of 17 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 17 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  7 * 10^0 * 981 = 6867
  running total = 16677
So F = 16677 centiNewtons = 166.77 N.
Final: \boxed{166.77}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  34,56 -> 5634
  83,42 -> 4283
  29,37 -> 3729
Apply to: 77,33
### Reasoning:
<|cot_start|>Examples:
  34,56 -> 5634
  83,42 -> 4283
  29,37 -> 3729
Check both candidate forms:
  concat(34,56)=3456  rev_concat(34,56)=5634  target=5634  rev_concat
  concat(83,42)=8342  rev_concat(83,42)=4283  target=4283  rev_concat
  concat(29,37)=2937  rev_concat(29,37)=3729  target=3729  rev_concat
Conclude operator: rev_concat.
Apply to (77, 33):  answer = 3377
Final: \boxed{3377}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01111011 -> 10111101
  00101110 -> 00010111
  01001110 -> 00100111
Apply to: 11001111
### Reasoning:
<|cot_start|>Given examples:
  01111011 -> 10111101
  00101110 -> 00010111
  01001110 -> 00100111
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 1,0,0
  bit 1: 1,0,1 -> 0,0,0
  bit 2: 1,1,0 -> 1,0,1
  bit 3: 1,0,0 -> 1,1,0
  bit 4: 1,1,1 -> 1,0,0
  bit 5: 0,1,1 -> 1,1,1
  bit 6: 1,1,1 -> 0,1,1
  bit 7: 1,0,0 -> 1,1,1
Deduce rule: rotate right 1.
Apply to 11001111:
  result = 11100111
Final: \boxed{11100111}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  qsfe qnaonxfa eykl guonfyyg
### Reasoning:
<|cot_start|>Cipher text: qsfe qnaonxfa eykl guonfyyg
Try each candidate Wonderland word against each ciphertext word:
  cipher='qsfe' candidate='alice' length-match=False
  cipher='qsfe' candidate='rabbit' length-match=False
  cipher='qsfe' candidate='hatter' length-match=False
  cipher='qsfe' candidate='cheshire' length-match=False
  cipher='qsfe' candidate='queen' length-match=False
  cipher='qsfe' candidate='tea' length-match=False
  cipher='qsfe' candidate='cake' length-match=True
  cipher='qsfe' candidate='garden' length-match=False
  cipher='qsfe' candidate='mushroom' length-match=False
  cipher='qsfe' candidate='card' length-match=True  <- assign
  cipher='qsfe' candidate='card' length-match=True  <- assign
  cipher='qsfe' candidate='wonderland' length-match=False
  cipher='qsfe' candidate='white' length-match=False
  cipher='qsfe' candidate='down' length-match=True
  cipher='qsfe' candidate='smile' length-match=False
  cipher='qsfe' candidate='smiled' length-match=False
  cipher='qsfe' candidate='looking' length-match=False
  cipher='qsfe' candidate='glass' length-match=False
  cipher='qsfe' candidate='march' length-match=False
  cipher='qsfe' candidate='hare' length-match=True
  cipher='qsfe' candidate='dormouse' length-match=False
  cipher='qnaonxfa' candidate='alice' length-match=False
  cipher='qnaonxfa' candidate='rabbit' length-match=False
  cipher='qnaonxfa' candidate='hatter' length-match=False
  cipher='qnaonxfa' candidate='cheshire' length-match=True  <- assign
  cipher='qnaonxfa' candidate='queen' length-match=False
  cipher='qnaonxfa' candidate='tea' length-match=False
  cipher='qnaonxfa' candidate='cake' length-match=False
  cipher='qnaonxfa' candidate='garden' length-match=False
  cipher='qnaonxfa' candidate='mushroom' length-match=True
  cipher='qnaonxfa' candidate='card' length-match=False
  cipher='qnaonxfa' candidate='card' length-match=False
  cipher='qnaonxfa' candidate='wonderland' length-match=False
  cipher='qnaonxfa' candidate='white' length-match=False
  cipher='qnaonxfa' candidate='down' length-match=False
  cipher='qnaonxfa' candidate='smile' length-match=False
  cipher='qnaonxfa' candidate='smiled' length-match=False
  cipher='qnaonxfa' candidate='looking' length-match=False
  cipher='qnaonxfa' candidate='glass' length-match=False
  cipher='qnaonxfa' candidate='march' length-match=False
  cipher='qnaonxfa' candidate='hare' length-match=False
  cipher='qnaonxfa' candidate='dormouse' length-match=True
  cipher='eykl' candidate='alice' length-match=False
  cipher='eykl' candidate='rabbit' length-match=False
  cipher='eykl' candidate='hatter' length-match=False
  cipher='eykl' candidate='cheshire' length-match=False
  cipher='eykl' candidate='queen' length-match=False
  cipher='eykl' candidate='tea' length-match=False
  cipher='eykl' candidate='cake' length-match=True
  cipher='eykl' candidate='garden' length-match=False
  cipher='eykl' candidate='mushroom' length-match=False
  cipher='eykl' candidate='card' length-match=True
  cipher='eykl' candidate='card' length-match=True
  cipher='eykl' candidate='wonderland' length-match=False
  cipher='eykl' candidate='white' length-match=False
  cipher='eykl' candidate='down' length-match=True  <- assign
  cipher='eykl' candidate='smile' length-match=False
  cipher='eykl' candidate='smiled' length-match=False
  cipher='eykl' candidate='looking' length-match=False
  cipher='eykl' candidate='glass' length-match=False
  cipher='eykl' candidate='march' length-match=False
  cipher='eykl' candidate='hare' length-match=True
  cipher='eykl' candidate='dormouse' length-match=False
  cipher='guonfyyg' candidate='alice' length-match=False
  cipher='guonfyyg' candidate='rabbit' length-match=False
  cipher='guonfyyg' candidate='hatter' length-match=False
  cipher='guonfyyg' candidate='cheshire' length-match=True
  cipher='guonfyyg' candidate='queen' length-match=False
  cipher='guonfyyg' candidate='tea' length-match=False
  cipher='guonfyyg' candidate='cake' length-match=False
  cipher='guonfyyg' candidate='garden' length-match=False
  cipher='guonfyyg' candidate='mushroom' length-match=True  <- assign
  cipher='guonfyyg' candidate='card' length-match=False
  cipher='guonfyyg' candidate='card' length-match=False
  cipher='guonfyyg' candidate='wonderland' length-match=False
  cipher='guonfyyg' candidate='white' length-match=False
  cipher='guonfyyg' candidate='down' length-match=False
  cipher='guonfyyg' candidate='smile' length-match=False
  cipher='guonfyyg' candidate='smiled' length-match=False
  cipher='guonfyyg' candidate='looking' length-match=False
  cipher='guonfyyg' candidate='glass' length-match=False
  cipher='guonfyyg' candidate='march' length-match=False
  cipher='guonfyyg' candidate='hare' length-match=False
  cipher='guonfyyg' candidate='dormouse' length-match=True
Assemble the decoded sentence:
  card cheshire down mushroom
Final: \boxed{card cheshire down mushroom}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  76,95 -> 171
  12,73 -> 85
  40,45 -> 85
Apply to: 75,48
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  76,95: '+' gives 171; target=171  MATCH
  76,95: '-' gives 19; target=171  no
  76,95: '*' gives 7220; target=171  no
  76,95: 'concat' gives 7695; target=171  no
  76,95: 'rev_concat' gives 9576; target=171  no
  76,95: 'max*min+sum' gives 7391; target=171  no
  76,95: 'digitsum2' gives 729; target=171  no
  12,73: '+' gives 85; target=85  MATCH
  12,73: '-' gives 61; target=85  no
  12,73: '*' gives 876; target=85  no
  12,73: 'concat' gives 1273; target=85  no
  12,73: 'rev_concat' gives 7312; target=85  no
  12,73: 'max*min+sum' gives 961; target=85  no
  12,73: 'digitsum2' gives 169; target=85  no
  40,45: '+' gives 85; target=85  MATCH
  40,45: '-' gives 5; target=85  no
  40,45: '*' gives 1800; target=85  no
  40,45: 'concat' gives 4045; target=85  no
  40,45: 'rev_concat' gives 4540; target=85  no
  40,45: 'max*min+sum' gives 1885; target=85  no
  40,45: 'digitsum2' gives 169; target=85  no
The only operator consistent with all examples is '+'.
Apply to (75, 48):
  result = 123
Final: \boxed{123}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  txgeur hwmau oimpu ijowgcci
### Reasoning:
<|cot_start|>Cipher text: txgeur hwmau oimpu ijowgcci
Try each candidate Wonderland word against each ciphertext word:
  cipher='txgeur' candidate='alice' length-match=False
  cipher='txgeur' candidate='rabbit' length-match=True
  cipher='txgeur' candidate='hatter' length-match=True
  cipher='txgeur' candidate='cheshire' length-match=False
  cipher='txgeur' candidate='queen' length-match=False
  cipher='txgeur' candidate='tea' length-match=False
  cipher='txgeur' candidate='cake' length-match=False
  cipher='txgeur' candidate='garden' length-match=True  <- assign
  cipher='txgeur' candidate='mushroom' length-match=False
  cipher='txgeur' candidate='card' length-match=False
  cipher='txgeur' candidate='card' length-match=False
  cipher='txgeur' candidate='wonderland' length-match=False
  cipher='txgeur' candidate='white' length-match=False
  cipher='txgeur' candidate='down' length-match=False
  cipher='txgeur' candidate='smile' length-match=False
  cipher='txgeur' candidate='smiled' length-match=True
  cipher='txgeur' candidate='looking' length-match=False
  cipher='txgeur' candidate='glass' length-match=False
  cipher='txgeur' candidate='march' length-match=False
  cipher='txgeur' candidate='hare' length-match=False
  cipher='txgeur' candidate='dormouse' length-match=False
  cipher='hwmau' candidate='alice' length-match=True
  cipher='hwmau' candidate='rabbit' length-match=False
  cipher='hwmau' candidate='hatter' length-match=False
  cipher='hwmau' candidate='cheshire' length-match=False
  cipher='hwmau' candidate='queen' length-match=True
  cipher='hwmau' candidate='tea' length-match=False
  cipher='hwmau' candidate='cake' length-match=False
  cipher='hwmau' candidate='garden' length-match=False
  cipher='hwmau' candidate='mushroom' length-match=False
  cipher='hwmau' candidate='card' length-match=False
  cipher='hwmau' candidate='card' length-match=False
  cipher='hwmau' candidate='wonderland' length-match=False
  cipher='hwmau' candidate='white' length-match=True  <- assign
  cipher='hwmau' candidate='down' length-match=False
  cipher='hwmau' candidate='smile' length-match=True
  cipher='hwmau' candidate='smiled' length-match=False
  cipher='hwmau' candidate='looking' length-match=False
  cipher='hwmau' candidate='glass' length-match=True
  cipher='hwmau' candidate='march' length-match=True
  cipher='hwmau' candidate='hare' length-match=False
  cipher='hwmau' candidate='dormouse' length-match=False
  cipher='oimpu' candidate='alice' length-match=True
  cipher='oimpu' candidate='rabbit' length-match=False
  cipher='oimpu' candidate='hatter' length-match=False
  cipher='oimpu' candidate='cheshire' length-match=False
  cipher='oimpu' candidate='queen' length-match=True
  cipher='oimpu' candidate='tea' length-match=False
  cipher='oimpu' candidate='cake' length-match=False
  cipher='oimpu' candidate='garden' length-match=False
  cipher='oimpu' candidate='mushroom' length-match=False
  cipher='oimpu' candidate='card' length-match=False
  cipher='oimpu' candidate='card' length-match=False
  cipher='oimpu' candidate='wonderland' length-match=False
  cipher='oimpu' candidate='white' length-match=True
  cipher='oimpu' candidate='down' length-match=False
  cipher='oimpu' candidate='smile' length-match=True  <- assign
  cipher='oimpu' candidate='smiled' length-match=False
  cipher='oimpu' candidate='looking' length-match=False
  cipher='oimpu' candidate='glass' length-match=True
  cipher='oimpu' candidate='march' length-match=True
  cipher='oimpu' candidate='hare' length-match=False
  cipher='oimpu' candidate='dormouse' length-match=False
  cipher='ijowgcci' candidate='alice' length-match=False
  cipher='ijowgcci' candidate='rabbit' length-match=False
  cipher='ijowgcci' candidate='hatter' length-match=False
  cipher='ijowgcci' candidate='cheshire' length-match=True
  cipher='ijowgcci' candidate='queen' length-match=False
  cipher='ijowgcci' candidate='tea' length-match=False
  cipher='ijowgcci' candidate='cake' length-match=False
  cipher='ijowgcci' candidate='garden' length-match=False
  cipher='ijowgcci' candidate='mushroom' length-match=True  <- assign
  cipher='ijowgcci' candidate='card' length-match=False
  cipher='ijowgcci' candidate='card' length-match=False
  cipher='ijowgcci' candidate='wonderland' length-match=False
  cipher='ijowgcci' candidate='white' length-match=False
  cipher='ijowgcci' candidate='down' length-match=False
  cipher='ijowgcci' candidate='smile' length-match=False
  cipher='ijowgcci' candidate='smiled' length-match=False
  cipher='ijowgcci' candidate='looking' length-match=False
  cipher='ijowgcci' candidate='glass' length-match=False
  cipher='ijowgcci' candidate='march' length-match=False
  cipher='ijowgcci' candidate='hare' length-match=False
  cipher='ijowgcci' candidate='dormouse' length-match=True
Assemble the decoded sentence:
  garden white smile mushroom
Final: \boxed{garden white smile mushroom}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  kliiyh rwvjwykv jcyovn xevvg
### Reasoning:
<|cot_start|>Cipher text: kliiyh rwvjwykv jcyovn xevvg
Try each candidate Wonderland word against each ciphertext word:
  cipher='kliiyh' candidate='alice' length-match=False
  cipher='kliiyh' candidate='rabbit' length-match=True  <- assign
  cipher='kliiyh' candidate='hatter' length-match=True
  cipher='kliiyh' candidate='cheshire' length-match=False
  cipher='kliiyh' candidate='queen' length-match=False
  cipher='kliiyh' candidate='tea' length-match=False
  cipher='kliiyh' candidate='cake' length-match=False
  cipher='kliiyh' candidate='garden' length-match=True
  cipher='kliiyh' candidate='mushroom' length-match=False
  cipher='kliiyh' candidate='card' length-match=False
  cipher='kliiyh' candidate='card' length-match=False
  cipher='kliiyh' candidate='wonderland' length-match=False
  cipher='kliiyh' candidate='white' length-match=False
  cipher='kliiyh' candidate='down' length-match=False
  cipher='kliiyh' candidate='smile' length-match=False
  cipher='kliiyh' candidate='smiled' length-match=True
  cipher='kliiyh' candidate='looking' length-match=False
  cipher='kliiyh' candidate='glass' length-match=False
  cipher='kliiyh' candidate='march' length-match=False
  cipher='kliiyh' candidate='hare' length-match=False
  cipher='kliiyh' candidate='dormouse' length-match=False
  cipher='rwvjwykv' candidate='alice' length-match=False
  cipher='rwvjwykv' candidate='rabbit' length-match=False
  cipher='rwvjwykv' candidate='hatter' length-match=False
  cipher='rwvjwykv' candidate='cheshire' length-match=True  <- assign
  cipher='rwvjwykv' candidate='queen' length-match=False
  cipher='rwvjwykv' candidate='tea' length-match=False
  cipher='rwvjwykv' candidate='cake' length-match=False
  cipher='rwvjwykv' candidate='garden' length-match=False
  cipher='rwvjwykv' candidate='mushroom' length-match=True
  cipher='rwvjwykv' candidate='card' length-match=False
  cipher='rwvjwykv' candidate='card' length-match=False
  cipher='rwvjwykv' candidate='wonderland' length-match=False
  cipher='rwvjwykv' candidate='white' length-match=False
  cipher='rwvjwykv' candidate='down' length-match=False
  cipher='rwvjwykv' candidate='smile' length-match=False
  cipher='rwvjwykv' candidate='smiled' length-match=False
  cipher='rwvjwykv' candidate='looking' length-match=False
  cipher='rwvjwykv' candidate='glass' length-match=False
  cipher='rwvjwykv' candidate='march' length-match=False
  cipher='rwvjwykv' candidate='hare' length-match=False
  cipher='rwvjwykv' candidate='dormouse' length-match=True
  cipher='jcyovn' candidate='alice' length-match=False
  cipher='jcyovn' candidate='rabbit' length-match=True
  cipher='jcyovn' candidate='hatter' length-match=True
  cipher='jcyovn' candidate='cheshire' length-match=False
  cipher='jcyovn' candidate='queen' length-match=False
  cipher='jcyovn' candidate='tea' length-match=False
  cipher='jcyovn' candidate='cake' length-match=False
  cipher='jcyovn' candidate='garden' length-match=True
  cipher='jcyovn' candidate='mushroom' length-match=False
  cipher='jcyovn' candidate='card' length-match=False
  cipher='jcyovn' candidate='card' length-match=False
  cipher='jcyovn' candidate='wonderland' length-match=False
  cipher='jcyovn' candidate='white' length-match=False
  cipher='jcyovn' candidate='down' length-match=False
  cipher='jcyovn' candidate='smile' length-match=False
  cipher='jcyovn' candidate='smiled' length-match=True  <- assign
  cipher='jcyovn' candidate='looking' length-match=False
  cipher='jcyovn' candidate='glass' length-match=False
  cipher='jcyovn' candidate='march' length-match=False
  cipher='jcyovn' candidate='hare' length-match=False
  cipher='jcyovn' candidate='dormouse' length-match=False
  cipher='xevvg' candidate='alice' length-match=True
  cipher='xevvg' candidate='rabbit' length-match=False
  cipher='xevvg' candidate='hatter' length-match=False
  cipher='xevvg' candidate='cheshire' length-match=False
  cipher='xevvg' candidate='queen' length-match=True  <- assign
  cipher='xevvg' candidate='tea' length-match=False
  cipher='xevvg' candidate='cake' length-match=False
  cipher='xevvg' candidate='garden' length-match=False
  cipher='xevvg' candidate='mushroom' length-match=False
  cipher='xevvg' candidate='card' length-match=False
  cipher='xevvg' candidate='card' length-match=False
  cipher='xevvg' candidate='wonderland' length-match=False
  cipher='xevvg' candidate='white' length-match=True
  cipher='xevvg' candidate='down' length-match=False
  cipher='xevvg' candidate='smile' length-match=True
  cipher='xevvg' candidate='smiled' length-match=False
  cipher='xevvg' candidate='looking' length-match=False
  cipher='xevvg' candidate='glass' length-match=True
  cipher='xevvg' candidate='march' length-match=True
  cipher='xevvg' candidate='hare' length-match=False
  cipher='xevvg' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  rabbit cheshire smiled queen
Final: \boxed{rabbit cheshire smiled queen}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  kutoq kutoqg ureca crlq
### Reasoning:
<|cot_start|>Cipher text: kutoq kutoqg ureca crlq
Try each candidate Wonderland word against each ciphertext word:
  cipher='kutoq' candidate='alice' length-match=True
  cipher='kutoq' candidate='rabbit' length-match=False
  cipher='kutoq' candidate='hatter' length-match=False
  cipher='kutoq' candidate='cheshire' length-match=False
  cipher='kutoq' candidate='queen' length-match=True
  cipher='kutoq' candidate='tea' length-match=False
  cipher='kutoq' candidate='cake' length-match=False
  cipher='kutoq' candidate='garden' length-match=False
  cipher='kutoq' candidate='mushroom' length-match=False
  cipher='kutoq' candidate='card' length-match=False
  cipher='kutoq' candidate='card' length-match=False
  cipher='kutoq' candidate='wonderland' length-match=False
  cipher='kutoq' candidate='white' length-match=True
  cipher='kutoq' candidate='down' length-match=False
  cipher='kutoq' candidate='smile' length-match=True  <- assign
  cipher='kutoq' candidate='smiled' length-match=False
  cipher='kutoq' candidate='looking' length-match=False
  cipher='kutoq' candidate='glass' length-match=True
  cipher='kutoq' candidate='march' length-match=True
  cipher='kutoq' candidate='hare' length-match=False
  cipher='kutoq' candidate='dormouse' length-match=False
  cipher='kutoqg' candidate='alice' length-match=False
  cipher='kutoqg' candidate='rabbit' length-match=True
  cipher='kutoqg' candidate='hatter' length-match=True
  cipher='kutoqg' candidate='cheshire' length-match=False
  cipher='kutoqg' candidate='queen' length-match=False
  cipher='kutoqg' candidate='tea' length-match=False
  cipher='kutoqg' candidate='cake' length-match=False
  cipher='kutoqg' candidate='garden' length-match=True
  cipher='kutoqg' candidate='mushroom' length-match=False
  cipher='kutoqg' candidate='card' length-match=False
  cipher='kutoqg' candidate='card' length-match=False
  cipher='kutoqg' candidate='wonderland' length-match=False
  cipher='kutoqg' candidate='white' length-match=False
  cipher='kutoqg' candidate='down' length-match=False
  cipher='kutoqg' candidate='smile' length-match=False
  cipher='kutoqg' candidate='smiled' length-match=True  <- assign
  cipher='kutoqg' candidate='looking' length-match=False
  cipher='kutoqg' candidate='glass' length-match=False
  cipher='kutoqg' candidate='march' length-match=False
  cipher='kutoqg' candidate='hare' length-match=False
  cipher='kutoqg' candidate='dormouse' length-match=False
  cipher='ureca' candidate='alice' length-match=True
  cipher='ureca' candidate='rabbit' length-match=False
  cipher='ureca' candidate='hatter' length-match=False
  cipher='ureca' candidate='cheshire' length-match=False
  cipher='ureca' candidate='queen' length-match=True
  cipher='ureca' candidate='tea' length-match=False
  cipher='ureca' candidate='cake' length-match=False
  cipher='ureca' candidate='garden' length-match=False
  cipher='ureca' candidate='mushroom' length-match=False
  cipher='ureca' candidate='card' length-match=False
  cipher='ureca' candidate='card' length-match=False
  cipher='ureca' candidate='wonderland' length-match=False
  cipher='ureca' candidate='white' length-match=True
  cipher='ureca' candidate='down' length-match=False
  cipher='ureca' candidate='smile' length-match=True
  cipher='ureca' candidate='smiled' length-match=False
  cipher='ureca' candidate='looking' length-match=False
  cipher='ureca' candidate='glass' length-match=True
  cipher='ureca' candidate='march' length-match=True  <- assign
  cipher='ureca' candidate='hare' length-match=False
  cipher='ureca' candidate='dormouse' length-match=False
  cipher='crlq' candidate='alice' length-match=False
  cipher='crlq' candidate='rabbit' length-match=False
  cipher='crlq' candidate='hatter' length-match=False
  cipher='crlq' candidate='cheshire' length-match=False
  cipher='crlq' candidate='queen' length-match=False
  cipher='crlq' candidate='tea' length-match=False
  cipher='crlq' candidate='cake' length-match=True  <- assign
  cipher='crlq' candidate='garden' length-match=False
  cipher='crlq' candidate='mushroom' length-match=False
  cipher='crlq' candidate='card' length-match=True
  cipher='crlq' candidate='card' length-match=True
  cipher='crlq' candidate='wonderland' length-match=False
  cipher='crlq' candidate='white' length-match=False
  cipher='crlq' candidate='down' length-match=True
  cipher='crlq' candidate='smile' length-match=False
  cipher='crlq' candidate='smiled' length-match=False
  cipher='crlq' candidate='looking' length-match=False
  cipher='crlq' candidate='glass' length-match=False
  cipher='crlq' candidate='march' length-match=False
  cipher='crlq' candidate='hare' length-match=True
  cipher='crlq' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  smile smiled march cake
Final: \boxed{smile smiled march cake}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  atsftibs uvvlixe gqssx akls
### Reasoning:
<|cot_start|>Cipher text: atsftibs uvvlixe gqssx akls
Try each candidate Wonderland word against each ciphertext word:
  cipher='atsftibs' candidate='alice' length-match=False
  cipher='atsftibs' candidate='rabbit' length-match=False
  cipher='atsftibs' candidate='hatter' length-match=False
  cipher='atsftibs' candidate='cheshire' length-match=True  <- assign
  cipher='atsftibs' candidate='queen' length-match=False
  cipher='atsftibs' candidate='tea' length-match=False
  cipher='atsftibs' candidate='cake' length-match=False
  cipher='atsftibs' candidate='garden' length-match=False
  cipher='atsftibs' candidate='mushroom' length-match=True
  cipher='atsftibs' candidate='card' length-match=False
  cipher='atsftibs' candidate='card' length-match=False
  cipher='atsftibs' candidate='wonderland' length-match=False
  cipher='atsftibs' candidate='white' length-match=False
  cipher='atsftibs' candidate='down' length-match=False
  cipher='atsftibs' candidate='smile' length-match=False
  cipher='atsftibs' candidate='smiled' length-match=False
  cipher='atsftibs' candidate='looking' length-match=False
  cipher='atsftibs' candidate='glass' length-match=False
  cipher='atsftibs' candidate='march' length-match=False
  cipher='atsftibs' candidate='hare' length-match=False
  cipher='atsftibs' candidate='dormouse' length-match=True
  cipher='uvvlixe' candidate='alice' length-match=False
  cipher='uvvlixe' candidate='rabbit' length-match=False
  cipher='uvvlixe' candidate='hatter' length-match=False
  cipher='uvvlixe' candidate='cheshire' length-match=False
  cipher='uvvlixe' candidate='queen' length-match=False
  cipher='uvvlixe' candidate='tea' length-match=False
  cipher='uvvlixe' candidate='cake' length-match=False
  cipher='uvvlixe' candidate='garden' length-match=False
  cipher='uvvlixe' candidate='mushroom' length-match=False
  cipher='uvvlixe' candidate='card' length-match=False
  cipher='uvvlixe' candidate='card' length-match=False
  cipher='uvvlixe' candidate='wonderland' length-match=False
  cipher='uvvlixe' candidate='white' length-match=False
  cipher='uvvlixe' candidate='down' length-match=False
  cipher='uvvlixe' candidate='smile' length-match=False
  cipher='uvvlixe' candidate='smiled' length-match=False
  cipher='uvvlixe' candidate='looking' length-match=True  <- assign
  cipher='uvvlixe' candidate='glass' length-match=False
  cipher='uvvlixe' candidate='march' length-match=False
  cipher='uvvlixe' candidate='hare' length-match=False
  cipher='uvvlixe' candidate='dormouse' length-match=False
  cipher='gqssx' candidate='alice' length-match=True
  cipher='gqssx' candidate='rabbit' length-match=False
  cipher='gqssx' candidate='hatter' length-match=False
  cipher='gqssx' candidate='cheshire' length-match=False
  cipher='gqssx' candidate='queen' length-match=True  <- assign
  cipher='gqssx' candidate='tea' length-match=False
  cipher='gqssx' candidate='cake' length-match=False
  cipher='gqssx' candidate='garden' length-match=False
  cipher='gqssx' candidate='mushroom' length-match=False
  cipher='gqssx' candidate='card' length-match=False
  cipher='gqssx' candidate='card' length-match=False
  cipher='gqssx' candidate='wonderland' length-match=False
  cipher='gqssx' candidate='white' length-match=True
  cipher='gqssx' candidate='down' length-match=False
  cipher='gqssx' candidate='smile' length-match=True
  cipher='gqssx' candidate='smiled' length-match=False
  cipher='gqssx' candidate='looking' length-match=False
  cipher='gqssx' candidate='glass' length-match=True
  cipher='gqssx' candidate='march' length-match=True
  cipher='gqssx' candidate='hare' length-match=False
  cipher='gqssx' candidate='dormouse' length-match=False
  cipher='akls' candidate='alice' length-match=False
  cipher='akls' candidate='rabbit' length-match=False
  cipher='akls' candidate='hatter' length-match=False
  cipher='akls' candidate='cheshire' length-match=False
  cipher='akls' candidate='queen' length-match=False
  cipher='akls' candidate='tea' length-match=False
  cipher='akls' candidate='cake' length-match=True  <- assign
  cipher='akls' candidate='garden' length-match=False
  cipher='akls' candidate='mushroom' length-match=False
  cipher='akls' candidate='card' length-match=True
  cipher='akls' candidate='card' length-match=True
  cipher='akls' candidate='wonderland' length-match=False
  cipher='akls' candidate='white' length-match=False
  cipher='akls' candidate='down' length-match=True
  cipher='akls' candidate='smile' length-match=False
  cipher='akls' candidate='smiled' length-match=False
  cipher='akls' candidate='looking' length-match=False
  cipher='akls' candidate='glass' length-match=False
  cipher='akls' candidate='march' length-match=False
  cipher='akls' candidate='hare' length-match=True
  cipher='akls' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  cheshire looking queen cake
Final: \boxed{cheshire looking queen cake}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  48,13 -> 35
  50,24 -> 26
  26,89 -> 63
Apply to: 91,77
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  48,13: '+' gives 61; target=35  no
  48,13: '-' gives 35; target=35  MATCH
  48,13: '*' gives 624; target=35  no
  48,13: 'concat' gives 4813; target=35  no
  48,13: 'rev_concat' gives 1348; target=35  no
  48,13: 'max*min+sum' gives 685; target=35  no
  48,13: 'digitsum2' gives 256; target=35  no
  50,24: '+' gives 74; target=26  no
  50,24: '-' gives 26; target=26  MATCH
  50,24: '*' gives 1200; target=26  no
  50,24: 'concat' gives 5024; target=26  no
  50,24: 'rev_concat' gives 2450; target=26  no
  50,24: 'max*min+sum' gives 1274; target=26  no
  50,24: 'digitsum2' gives 121; target=26  no
  26,89: '+' gives 115; target=63  no
  26,89: '-' gives 63; target=63  MATCH
  26,89: '*' gives 2314; target=63  no
  26,89: 'concat' gives 2689; target=63  no
  26,89: 'rev_concat' gives 8926; target=63  no
  26,89: 'max*min+sum' gives 2429; target=63  no
  26,89: 'digitsum2' gives 625; target=63  no
The only operator consistent with all examples is '-'.
Apply to (91, 77):
  result = 14
Final: \boxed{14}


### Task: unit
### Problem:
Convert 69 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 69 litres = 69 * 1000 millilitres.
Compute step by step:
  6 * 10^1 * 1000 = 60000
  running total = 60000
  9 * 10^0 * 1000 = 9000
  running total = 69000
Final: \boxed{69000}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11000011 -> 11000011
  01110110 -> 01101110
  10010000 -> 00001001
Apply to: 11111000
### Reasoning:
<|cot_start|>Given examples:
  11000011 -> 11000011
  01110110 -> 01101110
  10010000 -> 00001001
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 1,0,0
  bit 1: 1,1,0 -> 1,1,0
  bit 2: 0,1,0 -> 0,1,0
  bit 3: 0,1,1 -> 0,0,0
  bit 4: 0,0,0 -> 0,1,1
  bit 5: 0,1,0 -> 0,1,0
  bit 6: 1,1,0 -> 1,1,0
  bit 7: 1,0,0 -> 1,0,1
Deduce rule: reverse bits.
Apply to 11111000:
  result = 00011111
Final: \boxed{00011111}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  69,35 -> 3569
  98,33 -> 3398
  73,68 -> 6873
Apply to: 14,62
### Reasoning:
<|cot_start|>Examples:
  69,35 -> 3569
  98,33 -> 3398
  73,68 -> 6873
Check both candidate forms:
  concat(69,35)=6935  rev_concat(69,35)=3569  target=3569  rev_concat
  concat(98,33)=9833  rev_concat(98,33)=3398  target=3398  rev_concat
  concat(73,68)=7368  rev_concat(73,68)=6873  target=6873  rev_concat
Conclude operator: rev_concat.
Apply to (14, 62):  answer = 6214
Final: \boxed{6214}


### Task: numeral
### Problem:
Convert the Roman numeral I to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  I = 1  ->  0 + 1 = 1
Final: \boxed{1}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  oayr kammrq gsrrv bujv
### Reasoning:
<|cot_start|>Cipher text: oayr kammrq gsrrv bujv
Try each candidate Wonderland word against each ciphertext word:
  cipher='oayr' candidate='alice' length-match=False
  cipher='oayr' candidate='rabbit' length-match=False
  cipher='oayr' candidate='hatter' length-match=False
  cipher='oayr' candidate='cheshire' length-match=False
  cipher='oayr' candidate='queen' length-match=False
  cipher='oayr' candidate='tea' length-match=False
  cipher='oayr' candidate='cake' length-match=True  <- assign
  cipher='oayr' candidate='garden' length-match=False
  cipher='oayr' candidate='mushroom' length-match=False
  cipher='oayr' candidate='card' length-match=True
  cipher='oayr' candidate='card' length-match=True
  cipher='oayr' candidate='wonderland' length-match=False
  cipher='oayr' candidate='white' length-match=False
  cipher='oayr' candidate='down' length-match=True
  cipher='oayr' candidate='smile' length-match=False
  cipher='oayr' candidate='smiled' length-match=False
  cipher='oayr' candidate='looking' length-match=False
  cipher='oayr' candidate='glass' length-match=False
  cipher='oayr' candidate='march' length-match=False
  cipher='oayr' candidate='hare' length-match=True
  cipher='oayr' candidate='dormouse' length-match=False
  cipher='kammrq' candidate='alice' length-match=False
  cipher='kammrq' candidate='rabbit' length-match=True
  cipher='kammrq' candidate='hatter' length-match=True  <- assign
  cipher='kammrq' candidate='cheshire' length-match=False
  cipher='kammrq' candidate='queen' length-match=False
  cipher='kammrq' candidate='tea' length-match=False
  cipher='kammrq' candidate='cake' length-match=False
  cipher='kammrq' candidate='garden' length-match=True
  cipher='kammrq' candidate='mushroom' length-match=False
  cipher='kammrq' candidate='card' length-match=False
  cipher='kammrq' candidate='card' length-match=False
  cipher='kammrq' candidate='wonderland' length-match=False
  cipher='kammrq' candidate='white' length-match=False
  cipher='kammrq' candidate='down' length-match=False
  cipher='kammrq' candidate='smile' length-match=False
  cipher='kammrq' candidate='smiled' length-match=True
  cipher='kammrq' candidate='looking' length-match=False
  cipher='kammrq' candidate='glass' length-match=False
  cipher='kammrq' candidate='march' length-match=False
  cipher='kammrq' candidate='hare' length-match=False
  cipher='kammrq' candidate='dormouse' length-match=False
  cipher='gsrrv' candidate='alice' length-match=True
  cipher='gsrrv' candidate='rabbit' length-match=False
  cipher='gsrrv' candidate='hatter' length-match=False
  cipher='gsrrv' candidate='cheshire' length-match=False
  cipher='gsrrv' candidate='queen' length-match=True  <- assign
  cipher='gsrrv' candidate='tea' length-match=False
  cipher='gsrrv' candidate='cake' length-match=False
  cipher='gsrrv' candidate='garden' length-match=False
  cipher='gsrrv' candidate='mushroom' length-match=False
  cipher='gsrrv' candidate='card' length-match=False
  cipher='gsrrv' candidate='card' length-match=False
  cipher='gsrrv' candidate='wonderland' length-match=False
  cipher='gsrrv' candidate='white' length-match=True
  cipher='gsrrv' candidate='down' length-match=False
  cipher='gsrrv' candidate='smile' length-match=True
  cipher='gsrrv' candidate='smiled' length-match=False
  cipher='gsrrv' candidate='looking' length-match=False
  cipher='gsrrv' candidate='glass' length-match=True
  cipher='gsrrv' candidate='march' length-match=True
  cipher='gsrrv' candidate='hare' length-match=False
  cipher='gsrrv' candidate='dormouse' length-match=False
  cipher='bujv' candidate='alice' length-match=False
  cipher='bujv' candidate='rabbit' length-match=False
  cipher='bujv' candidate='hatter' length-match=False
  cipher='bujv' candidate='cheshire' length-match=False
  cipher='bujv' candidate='queen' length-match=False
  cipher='bujv' candidate='tea' length-match=False
  cipher='bujv' candidate='cake' length-match=True
  cipher='bujv' candidate='garden' length-match=False
  cipher='bujv' candidate='mushroom' length-match=False
  cipher='bujv' candidate='card' length-match=True
  cipher='bujv' candidate='card' length-match=True
  cipher='bujv' candidate='wonderland' length-match=False
  cipher='bujv' candidate='white' length-match=False
  cipher='bujv' candidate='down' length-match=True  <- assign
  cipher='bujv' candidate='smile' length-match=False
  cipher='bujv' candidate='smiled' length-match=False
  cipher='bujv' candidate='looking' length-match=False
  cipher='bujv' candidate='glass' length-match=False
  cipher='bujv' candidate='march' length-match=False
  cipher='bujv' candidate='hare' length-match=True
  cipher='bujv' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  cake hatter queen down
Final: \boxed{cake hatter queen down}


### Task: numeral
### Problem:
Convert the Roman numeral LXXXVIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  X = 10  ->  60 + 10 = 70
  X = 10  ->  70 + 10 = 80
  V = 5  ->  80 + 5 = 85
  I = 1  ->  85 + 1 = 86
  I = 1  ->  86 + 1 = 87
  I = 1  ->  87 + 1 = 88
Final: \boxed{88}


### Task: gravity
### Problem:
A mass of 27 kg is in free fall.  Compute the gravitational force in Newtons (g = 9.81 m/s^2).
### Reasoning:
<|cot_start|>Use g = 9.81 m/s^2  (work in cN = 100x N to stay integer).
F = m * g_cN = 27 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  7 * 10^0 * 981 = 6867
  running total = 26487
So F = 26487 centiNewtons = 264.87 N.
Final: \boxed{264.87}


### Task: unit
### Problem:
Convert 19 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 19 kilometres = 19 * 1000 metres.
Compute step by step:
  1 * 10^1 * 1000 = 10000
  running total = 10000
  9 * 10^0 * 1000 = 9000
  running total = 19000
Final: \boxed{19000}


### Task: unit
### Problem:
Convert 25 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 25 kilometres = 25 * 1000 metres.
Compute step by step:
  2 * 10^1 * 1000 = 20000
  running total = 20000
  5 * 10^0 * 1000 = 5000
  running total = 25000
Final: \boxed{25000}


### Task: numeral
### Problem:
Convert the Roman numeral LXXI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  X = 10  ->  60 + 10 = 70
  I = 1  ->  70 + 1 = 71
Final: \boxed{71}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  adzserpizs virs cuype fteez
### Reasoning:
<|cot_start|>Cipher text: adzserpizs virs cuype fteez
Try each candidate Wonderland word against each ciphertext word:
  cipher='adzserpizs' candidate='alice' length-match=False
  cipher='adzserpizs' candidate='rabbit' length-match=False
  cipher='adzserpizs' candidate='hatter' length-match=False
  cipher='adzserpizs' candidate='cheshire' length-match=False
  cipher='adzserpizs' candidate='queen' length-match=False
  cipher='adzserpizs' candidate='tea' length-match=False
  cipher='adzserpizs' candidate='cake' length-match=False
  cipher='adzserpizs' candidate='garden' length-match=False
  cipher='adzserpizs' candidate='mushroom' length-match=False
  cipher='adzserpizs' candidate='card' length-match=False
  cipher='adzserpizs' candidate='card' length-match=False
  cipher='adzserpizs' candidate='wonderland' length-match=True  <- assign
  cipher='adzserpizs' candidate='white' length-match=False
  cipher='adzserpizs' candidate='down' length-match=False
  cipher='adzserpizs' candidate='smile' length-match=False
  cipher='adzserpizs' candidate='smiled' length-match=False
  cipher='adzserpizs' candidate='looking' length-match=False
  cipher='adzserpizs' candidate='glass' length-match=False
  cipher='adzserpizs' candidate='march' length-match=False
  cipher='adzserpizs' candidate='hare' length-match=False
  cipher='adzserpizs' candidate='dormouse' length-match=False
  cipher='virs' candidate='alice' length-match=False
  cipher='virs' candidate='rabbit' length-match=False
  cipher='virs' candidate='hatter' length-match=False
  cipher='virs' candidate='cheshire' length-match=False
  cipher='virs' candidate='queen' length-match=False
  cipher='virs' candidate='tea' length-match=False
  cipher='virs' candidate='cake' length-match=True
  cipher='virs' candidate='garden' length-match=False
  cipher='virs' candidate='mushroom' length-match=False
  cipher='virs' candidate='card' length-match=True  <- assign
  cipher='virs' candidate='card' length-match=True  <- assign
  cipher='virs' candidate='wonderland' length-match=False
  cipher='virs' candidate='white' length-match=False
  cipher='virs' candidate='down' length-match=True
  cipher='virs' candidate='smile' length-match=False
  cipher='virs' candidate='smiled' length-match=False
  cipher='virs' candidate='looking' length-match=False
  cipher='virs' candidate='glass' length-match=False
  cipher='virs' candidate='march' length-match=False
  cipher='virs' candidate='hare' length-match=True
  cipher='virs' candidate='dormouse' length-match=False
  cipher='cuype' candidate='alice' length-match=True
  cipher='cuype' candidate='rabbit' length-match=False
  cipher='cuype' candidate='hatter' length-match=False
  cipher='cuype' candidate='cheshire' length-match=False
  cipher='cuype' candidate='queen' length-match=True
  cipher='cuype' candidate='tea' length-match=False
  cipher='cuype' candidate='cake' length-match=False
  cipher='cuype' candidate='garden' length-match=False
  cipher='cuype' candidate='mushroom' length-match=False
  cipher='cuype' candidate='card' length-match=False
  cipher='cuype' candidate='card' length-match=False
  cipher='cuype' candidate='wonderland' length-match=False
  cipher='cuype' candidate='white' length-match=True
  cipher='cuype' candidate='down' length-match=False
  cipher='cuype' candidate='smile' length-match=True  <- assign
  cipher='cuype' candidate='smiled' length-match=False
  cipher='cuype' candidate='looking' length-match=False
  cipher='cuype' candidate='glass' length-match=True
  cipher='cuype' candidate='march' length-match=True
  cipher='cuype' candidate='hare' length-match=False
  cipher='cuype' candidate='dormouse' length-match=False
  cipher='fteez' candidate='alice' length-match=True
  cipher='fteez' candidate='rabbit' length-match=False
  cipher='fteez' candidate='hatter' length-match=False
  cipher='fteez' candidate='cheshire' length-match=False
  cipher='fteez' candidate='queen' length-match=True  <- assign
  cipher='fteez' candidate='tea' length-match=False
  cipher='fteez' candidate='cake' length-match=False
  cipher='fteez' candidate='garden' length-match=False
  cipher='fteez' candidate='mushroom' length-match=False
  cipher='fteez' candidate='card' length-match=False
  cipher='fteez' candidate='card' length-match=False
  cipher='fteez' candidate='wonderland' length-match=False
  cipher='fteez' candidate='white' length-match=True
  cipher='fteez' candidate='down' length-match=False
  cipher='fteez' candidate='smile' length-match=True
  cipher='fteez' candidate='smiled' length-match=False
  cipher='fteez' candidate='looking' length-match=False
  cipher='fteez' candidate='glass' length-match=True
  cipher='fteez' candidate='march' length-match=True
  cipher='fteez' candidate='hare' length-match=False
  cipher='fteez' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  wonderland card smile queen
Final: \boxed{wonderland card smile queen}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  gjen gunoukmn ajmgu gjmc
### Reasoning:
<|cot_start|>Cipher text: gjen gunoukmn ajmgu gjmc
Try each candidate Wonderland word against each ciphertext word:
  cipher='gjen' candidate='alice' length-match=False
  cipher='gjen' candidate='rabbit' length-match=False
  cipher='gjen' candidate='hatter' length-match=False
  cipher='gjen' candidate='cheshire' length-match=False
  cipher='gjen' candidate='queen' length-match=False
  cipher='gjen' candidate='tea' length-match=False
  cipher='gjen' candidate='cake' length-match=True  <- assign
  cipher='gjen' candidate='garden' length-match=False
  cipher='gjen' candidate='mushroom' length-match=False
  cipher='gjen' candidate='card' length-match=True
  cipher='gjen' candidate='card' length-match=True
  cipher='gjen' candidate='wonderland' length-match=False
  cipher='gjen' candidate='white' length-match=False
  cipher='gjen' candidate='down' length-match=True
  cipher='gjen' candidate='smile' length-match=False
  cipher='gjen' candidate='smiled' length-match=False
  cipher='gjen' candidate='looking' length-match=False
  cipher='gjen' candidate='glass' length-match=False
  cipher='gjen' candidate='march' length-match=False
  cipher='gjen' candidate='hare' length-match=True
  cipher='gjen' candidate='dormouse' length-match=False
  cipher='gunoukmn' candidate='alice' length-match=False
  cipher='gunoukmn' candidate='rabbit' length-match=False
  cipher='gunoukmn' candidate='hatter' length-match=False
  cipher='gunoukmn' candidate='cheshire' length-match=True  <- assign
  cipher='gunoukmn' candidate='queen' length-match=False
  cipher='gunoukmn' candidate='tea' length-match=False
  cipher='gunoukmn' candidate='cake' length-match=False
  cipher='gunoukmn' candidate='garden' length-match=False
  cipher='gunoukmn' candidate='mushroom' length-match=True
  cipher='gunoukmn' candidate='card' length-match=False
  cipher='gunoukmn' candidate='card' length-match=False
  cipher='gunoukmn' candidate='wonderland' length-match=False
  cipher='gunoukmn' candidate='white' length-match=False
  cipher='gunoukmn' candidate='down' length-match=False
  cipher='gunoukmn' candidate='smile' length-match=False
  cipher='gunoukmn' candidate='smiled' length-match=False
  cipher='gunoukmn' candidate='looking' length-match=False
  cipher='gunoukmn' candidate='glass' length-match=False
  cipher='gunoukmn' candidate='march' length-match=False
  cipher='gunoukmn' candidate='hare' length-match=False
  cipher='gunoukmn' candidate='dormouse' length-match=True
  cipher='ajmgu' candidate='alice' length-match=True
  cipher='ajmgu' candidate='rabbit' length-match=False
  cipher='ajmgu' candidate='hatter' length-match=False
  cipher='ajmgu' candidate='cheshire' length-match=False
  cipher='ajmgu' candidate='queen' length-match=True
  cipher='ajmgu' candidate='tea' length-match=False
  cipher='ajmgu' candidate='cake' length-match=False
  cipher='ajmgu' candidate='garden' length-match=False
  cipher='ajmgu' candidate='mushroom' length-match=False
  cipher='ajmgu' candidate='card' length-match=False
  cipher='ajmgu' candidate='card' length-match=False
  cipher='ajmgu' candidate='wonderland' length-match=False
  cipher='ajmgu' candidate='white' length-match=True
  cipher='ajmgu' candidate='down' length-match=False
  cipher='ajmgu' candidate='smile' length-match=True
  cipher='ajmgu' candidate='smiled' length-match=False
  cipher='ajmgu' candidate='looking' length-match=False
  cipher='ajmgu' candidate='glass' length-match=True
  cipher='ajmgu' candidate='march' length-match=True  <- assign
  cipher='ajmgu' candidate='hare' length-match=False
  cipher='ajmgu' candidate='dormouse' length-match=False
  cipher='gjmc' candidate='alice' length-match=False
  cipher='gjmc' candidate='rabbit' length-match=False
  cipher='gjmc' candidate='hatter' length-match=False
  cipher='gjmc' candidate='cheshire' length-match=False
  cipher='gjmc' candidate='queen' length-match=False
  cipher='gjmc' candidate='tea' length-match=False
  cipher='gjmc' candidate='cake' length-match=True
  cipher='gjmc' candidate='garden' length-match=False
  cipher='gjmc' candidate='mushroom' length-match=False
  cipher='gjmc' candidate='card' length-match=True  <- assign
  cipher='gjmc' candidate='card' length-match=True  <- assign
  cipher='gjmc' candidate='wonderland' length-match=False
  cipher='gjmc' candidate='white' length-match=False
  cipher='gjmc' candidate='down' length-match=True
  cipher='gjmc' candidate='smile' length-match=False
  cipher='gjmc' candidate='smiled' length-match=False
  cipher='gjmc' candidate='looking' length-match=False
  cipher='gjmc' candidate='glass' length-match=False
  cipher='gjmc' candidate='march' length-match=False
  cipher='gjmc' candidate='hare' length-match=True
  cipher='gjmc' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  cake cheshire march card
Final: \boxed{cake cheshire march card}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01000111 -> 00010010
  00001010 -> 01011111
  01000101 -> 00010000
Apply to: 00110100
### Reasoning:
<|cot_start|>Given examples:
  01000111 -> 00010010
  00001010 -> 01011111
  01000101 -> 00010000
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 0,0,0
  bit 1: 1,0,1 -> 0,1,0
  bit 2: 0,0,0 -> 0,0,0
  bit 3: 0,0,0 -> 1,1,1
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 1,0,1 -> 0,1,0
  bit 6: 1,1,0 -> 1,1,0
  bit 7: 1,0,1 -> 0,1,0
Deduce rule: xor 0x55.
Apply to 00110100:
  result = 01100001
Final: \boxed{01100001}


### Task: cipher
### Problem:
Decode the following substitution cipher (Wonderland themed):
  hxunpggh bsdoj obvj rjb
### Reasoning:
<|cot_start|>Cipher text: hxunpggh bsdoj obvj rjb
Try each candidate Wonderland word against each ciphertext word:
  cipher='hxunpggh' candidate='alice' length-match=False
  cipher='hxunpggh' candidate='rabbit' length-match=False
  cipher='hxunpggh' candidate='hatter' length-match=False
  cipher='hxunpggh' candidate='cheshire' length-match=True
  cipher='hxunpggh' candidate='queen' length-match=False
  cipher='hxunpggh' candidate='tea' length-match=False
  cipher='hxunpggh' candidate='cake' length-match=False
  cipher='hxunpggh' candidate='garden' length-match=False
  cipher='hxunpggh' candidate='mushroom' length-match=True  <- assign
  cipher='hxunpggh' candidate='card' length-match=False
  cipher='hxunpggh' candidate='card' length-match=False
  cipher='hxunpggh' candidate='wonderland' length-match=False
  cipher='hxunpggh' candidate='white' length-match=False
  cipher='hxunpggh' candidate='down' length-match=False
  cipher='hxunpggh' candidate='smile' length-match=False
  cipher='hxunpggh' candidate='smiled' length-match=False
  cipher='hxunpggh' candidate='looking' length-match=False
  cipher='hxunpggh' candidate='glass' length-match=False
  cipher='hxunpggh' candidate='march' length-match=False
  cipher='hxunpggh' candidate='hare' length-match=False
  cipher='hxunpggh' candidate='dormouse' length-match=True
  cipher='bsdoj' candidate='alice' length-match=True  <- assign
  cipher='bsdoj' candidate='rabbit' length-match=False
  cipher='bsdoj' candidate='hatter' length-match=False
  cipher='bsdoj' candidate='cheshire' length-match=False
  cipher='bsdoj' candidate='queen' length-match=True
  cipher='bsdoj' candidate='tea' length-match=False
  cipher='bsdoj' candidate='cake' length-match=False
  cipher='bsdoj' candidate='garden' length-match=False
  cipher='bsdoj' candidate='mushroom' length-match=False
  cipher='bsdoj' candidate='card' length-match=False
  cipher='bsdoj' candidate='card' length-match=False
  cipher='bsdoj' candidate='wonderland' length-match=False
  cipher='bsdoj' candidate='white' length-match=True
  cipher='bsdoj' candidate='down' length-match=False
  cipher='bsdoj' candidate='smile' length-match=True
  cipher='bsdoj' candidate='smiled' length-match=False
  cipher='bsdoj' candidate='looking' length-match=False
  cipher='bsdoj' candidate='glass' length-match=True
  cipher='bsdoj' candidate='march' length-match=True
  cipher='bsdoj' candidate='hare' length-match=False
  cipher='bsdoj' candidate='dormouse' length-match=False
  cipher='obvj' candidate='alice' length-match=False
  cipher='obvj' candidate='rabbit' length-match=False
  cipher='obvj' candidate='hatter' length-match=False
  cipher='obvj' candidate='cheshire' length-match=False
  cipher='obvj' candidate='queen' length-match=False
  cipher='obvj' candidate='tea' length-match=False
  cipher='obvj' candidate='cake' length-match=True  <- assign
  cipher='obvj' candidate='garden' length-match=False
  cipher='obvj' candidate='mushroom' length-match=False
  cipher='obvj' candidate='card' length-match=True
  cipher='obvj' candidate='card' length-match=True
  cipher='obvj' candidate='wonderland' length-match=False
  cipher='obvj' candidate='white' length-match=False
  cipher='obvj' candidate='down' length-match=True
  cipher='obvj' candidate='smile' length-match=False
  cipher='obvj' candidate='smiled' length-match=False
  cipher='obvj' candidate='looking' length-match=False
  cipher='obvj' candidate='glass' length-match=False
  cipher='obvj' candidate='march' length-match=False
  cipher='obvj' candidate='hare' length-match=True
  cipher='obvj' candidate='dormouse' length-match=False
  cipher='rjb' candidate='alice' length-match=False
  cipher='rjb' candidate='rabbit' length-match=False
  cipher='rjb' candidate='hatter' length-match=False
  cipher='rjb' candidate='cheshire' length-match=False
  cipher='rjb' candidate='queen' length-match=False
  cipher='rjb' candidate='tea' length-match=True  <- assign
  cipher='rjb' candidate='cake' length-match=False
  cipher='rjb' candidate='garden' length-match=False
  cipher='rjb' candidate='mushroom' length-match=False
  cipher='rjb' candidate='card' length-match=False
  cipher='rjb' candidate='card' length-match=False
  cipher='rjb' candidate='wonderland' length-match=False
  cipher='rjb' candidate='white' length-match=False
  cipher='rjb' candidate='down' length-match=False
  cipher='rjb' candidate='smile' length-match=False
  cipher='rjb' candidate='smiled' length-match=False
  cipher='rjb' candidate='looking' length-match=False
  cipher='rjb' candidate='glass' length-match=False
  cipher='rjb' candidate='march' length-match=False
  cipher='rjb' candidate='hare' length-match=False
  cipher='rjb' candidate='dormouse' length-match=False
Assemble the decoded sentence:
  mushroom alice cake tea
Final: \boxed{mushroom alice cake tea}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  01110000 -> 00100101
  00110001 -> 01100100
  01010100 -> 00000001
Apply to: 11101000
### Reasoning:
<|cot_start|>Given examples:
  01110000 -> 00100101
  00110001 -> 01100100
  01010100 -> 00000001
Compare each bit position across the three examples:
  bit 0: 0,0,0 -> 0,0,0
  bit 1: 1,0,1 -> 0,1,0
  bit 2: 1,1,0 -> 1,1,0
  bit 3: 1,1,1 -> 0,0,0
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 0,0,1 -> 1,1,0
  bit 6: 0,0,0 -> 0,0,0
  bit 7: 0,1,0 -> 1,0,1
Deduce rule: xor 0x55.
Apply to 11101000:
  result = 10111101
Final: \boxed{10111101}