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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  21,36 -> 3621
  15,91 -> 9115
  61,43 -> 4361
Apply to: 75,53
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  21,36: '+' gives 57; target=3621  no
  21,36: '-' gives 15; target=3621  no
  21,36: '*' gives 756; target=3621  no
  21,36: 'concat' gives 2136; target=3621  no
  21,36: 'rev_concat' gives 3621; target=3621  MATCH
  21,36: 'max*min+sum' gives 813; target=3621  no
  21,36: 'digitsum2' gives 144; target=3621  no
  15,91: '+' gives 106; target=9115  no
  15,91: '-' gives 76; target=9115  no
  15,91: '*' gives 1365; target=9115  no
  15,91: 'concat' gives 1591; target=9115  no
  15,91: 'rev_concat' gives 9115; target=9115  MATCH
  15,91: 'max*min+sum' gives 1471; target=9115  no
  15,91: 'digitsum2' gives 256; target=9115  no
  61,43: '+' gives 104; target=4361  no
  61,43: '-' gives 18; target=4361  no
  61,43: '*' gives 2623; target=4361  no
  61,43: 'concat' gives 6143; target=4361  no
  61,43: 'rev_concat' gives 4361; target=4361  MATCH
  61,43: 'max*min+sum' gives 2727; target=4361  no
  61,43: 'digitsum2' gives 196; target=4361  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (75, 53):
  result = 5375
Final: \boxed{5375}


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


### Task: gravity
### Problem:
A mass of 9 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 = 9 * 981.
Step-by-step multiplication:
  9 * 10^0 * 981 = 8829
  running total = 8829
So F = 8829 centiNewtons = 88.29 N.
Final: \boxed{88.29}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  94,35 -> 441
  76,47 -> 576
  83,82 -> 441
Apply to: 21,29
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  94,35: '+' gives 129; target=441  no
  94,35: '-' gives 59; target=441  no
  94,35: '*' gives 3290; target=441  no
  94,35: 'concat' gives 9435; target=441  no
  94,35: 'rev_concat' gives 3594; target=441  no
  94,35: 'max*min+sum' gives 3419; target=441  no
  94,35: 'digitsum2' gives 441; target=441  MATCH
  76,47: '+' gives 123; target=576  no
  76,47: '-' gives 29; target=576  no
  76,47: '*' gives 3572; target=576  no
  76,47: 'concat' gives 7647; target=576  no
  76,47: 'rev_concat' gives 4776; target=576  no
  76,47: 'max*min+sum' gives 3695; target=576  no
  76,47: 'digitsum2' gives 576; target=576  MATCH
  83,82: '+' gives 165; target=441  no
  83,82: '-' gives 1; target=441  no
  83,82: '*' gives 6806; target=441  no
  83,82: 'concat' gives 8382; target=441  no
  83,82: 'rev_concat' gives 8283; target=441  no
  83,82: 'max*min+sum' gives 6971; target=441  no
  83,82: 'digitsum2' gives 441; target=441  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (21, 29):
  result = 196
Final: \boxed{196}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  65,10 -> 6510
  88,39 -> 8839
  61,88 -> 6188
Apply to: 72,73
### Reasoning:
<|cot_start|>Examples:
  65,10 -> 6510
  88,39 -> 8839
  61,88 -> 6188
Check both candidate forms:
  concat(65,10)=6510  rev_concat(65,10)=1065  target=6510  concat
  concat(88,39)=8839  rev_concat(88,39)=3988  target=8839  concat
  concat(61,88)=6188  rev_concat(61,88)=8861  target=6188  concat
Conclude operator: concat.
Apply to (72, 73):  answer = 7273
Final: \boxed{7273}


### Task: gravity
### Problem:
A mass of 44 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 = 44 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  4 * 10^0 * 981 = 3924
  running total = 43164
So F = 43164 centiNewtons = 431.64 N.
Final: \boxed{431.64}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  47,79 -> 7947
  13,82 -> 8213
  16,61 -> 6116
Apply to: 62,77
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  47,79: '+' gives 126; target=7947  no
  47,79: '-' gives 32; target=7947  no
  47,79: '*' gives 3713; target=7947  no
  47,79: 'concat' gives 4779; target=7947  no
  47,79: 'rev_concat' gives 7947; target=7947  MATCH
  47,79: 'max*min+sum' gives 3839; target=7947  no
  47,79: 'digitsum2' gives 729; target=7947  no
  13,82: '+' gives 95; target=8213  no
  13,82: '-' gives 69; target=8213  no
  13,82: '*' gives 1066; target=8213  no
  13,82: 'concat' gives 1382; target=8213  no
  13,82: 'rev_concat' gives 8213; target=8213  MATCH
  13,82: 'max*min+sum' gives 1161; target=8213  no
  13,82: 'digitsum2' gives 196; target=8213  no
  16,61: '+' gives 77; target=6116  no
  16,61: '-' gives 45; target=6116  no
  16,61: '*' gives 976; target=6116  no
  16,61: 'concat' gives 1661; target=6116  no
  16,61: 'rev_concat' gives 6116; target=6116  MATCH
  16,61: 'max*min+sum' gives 1053; target=6116  no
  16,61: 'digitsum2' gives 196; target=6116  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (62, 77):
  result = 7762
Final: \boxed{7762}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00111010 -> 11111010
  01010111 -> 11110111
  11111110 -> 11111110
Apply to: 01100110
### Reasoning:
<|cot_start|>Given examples:
  00111010 -> 11111010
  01010111 -> 11110111
  11111110 -> 11111110
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,1
  bit 1: 0,1,1 -> 1,1,1
  bit 2: 1,0,1 -> 1,1,1
  bit 3: 1,1,1 -> 1,1,1
  bit 4: 1,0,1 -> 1,0,1
  bit 5: 0,1,1 -> 0,1,1
  bit 6: 1,1,1 -> 1,1,1
  bit 7: 0,1,0 -> 0,1,0
Deduce rule: or 0xF0.
Apply to 01100110:
  result = 11110110
Final: \boxed{11110110}


### Task: numeral
### Problem:
Convert the Roman numeral XCVII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  V = 5  ->  90 + 5 = 95
  I = 1  ->  95 + 1 = 96
  I = 1  ->  96 + 1 = 97
Final: \boxed{97}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  12,96 -> 9612
  58,50 -> 5058
  15,77 -> 7715
Apply to: 35,24
### Reasoning:
<|cot_start|>Examples:
  12,96 -> 9612
  58,50 -> 5058
  15,77 -> 7715
Check both candidate forms:
  concat(12,96)=1296  rev_concat(12,96)=9612  target=9612  rev_concat
  concat(58,50)=5850  rev_concat(58,50)=5058  target=5058  rev_concat
  concat(15,77)=1577  rev_concat(15,77)=7715  target=7715  rev_concat
Conclude operator: rev_concat.
Apply to (35, 24):  answer = 2435
Final: \boxed{2435}


### Task: unit
### Problem:
Convert 87 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 87 days = 87 * 24 hours.
Compute step by step:
  8 * 10^1 * 24 = 1920
  running total = 1920
  7 * 10^0 * 24 = 168
  running total = 2088
Final: \boxed{2088}


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


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  57,53 -> 5357
  21,83 -> 8321
  96,97 -> 9796
Apply to: 57,56
### Reasoning:
<|cot_start|>Examples:
  57,53 -> 5357
  21,83 -> 8321
  96,97 -> 9796
Check both candidate forms:
  concat(57,53)=5753  rev_concat(57,53)=5357  target=5357  rev_concat
  concat(21,83)=2183  rev_concat(21,83)=8321  target=8321  rev_concat
  concat(96,97)=9697  rev_concat(96,97)=9796  target=9796  rev_concat
Conclude operator: rev_concat.
Apply to (57, 56):  answer = 5657
Final: \boxed{5657}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11100111 -> 11110111
  01000011 -> 11110011
  00110001 -> 11110001
Apply to: 00000111
### Reasoning:
<|cot_start|>Given examples:
  11100111 -> 11110111
  01000011 -> 11110011
  00110001 -> 11110001
Compare each bit position across the three examples:
  bit 0: 1,0,0 -> 1,1,1
  bit 1: 1,1,0 -> 1,1,1
  bit 2: 1,0,1 -> 1,1,1
  bit 3: 0,0,1 -> 1,1,1
  bit 4: 0,0,0 -> 0,0,0
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 1,1,0 -> 1,1,0
  bit 7: 1,1,1 -> 1,1,1
Deduce rule: or 0xF0.
Apply to 00000111:
  result = 11110111
Final: \boxed{11110111}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  67,72 -> 7267
  31,37 -> 3731
  90,24 -> 2490
Apply to: 79,76
### Reasoning:
<|cot_start|>Examples:
  67,72 -> 7267
  31,37 -> 3731
  90,24 -> 2490
Check both candidate forms:
  concat(67,72)=6772  rev_concat(67,72)=7267  target=7267  rev_concat
  concat(31,37)=3137  rev_concat(31,37)=3731  target=3731  rev_concat
  concat(90,24)=9024  rev_concat(90,24)=2490  target=2490  rev_concat
Conclude operator: rev_concat.
Apply to (79, 76):  answer = 7679
Final: \boxed{7679}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  83,95 -> 9583
  57,42 -> 4257
  68,88 -> 8868
Apply to: 46,45
### Reasoning:
<|cot_start|>Examples:
  83,95 -> 9583
  57,42 -> 4257
  68,88 -> 8868
Check both candidate forms:
  concat(83,95)=8395  rev_concat(83,95)=9583  target=9583  rev_concat
  concat(57,42)=5742  rev_concat(57,42)=4257  target=4257  rev_concat
  concat(68,88)=6888  rev_concat(68,88)=8868  target=8868  rev_concat
Conclude operator: rev_concat.
Apply to (46, 45):  answer = 4546
Final: \boxed{4546}


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


### Task: numeral
### Problem:
Convert the Roman numeral XCI to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  XC = 90  ->  0 + 90 = 90
  I = 1  ->  90 + 1 = 91
Final: \boxed{91}


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


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


### Task: unit
### Problem:
Convert 90 metres to centimetres.
### Reasoning:
<|cot_start|>Conversion factor: 1 metres = 100 centimetres.
So 90 metres = 90 * 100 centimetres.
Compute step by step:
  9 * 10^1 * 100 = 9000
  running total = 9000
  0 * 10^0 * 100 = 0
  running total = 9000
Final: \boxed{9000}


### Task: unit
### Problem:
Convert 74 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 74 days = 74 * 24 hours.
Compute step by step:
  7 * 10^1 * 24 = 1680
  running total = 1680
  4 * 10^0 * 24 = 96
  running total = 1776
Final: \boxed{1776}


### Task: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  13,66 -> 1366
  45,48 -> 4548
  77,12 -> 7712
Apply to: 58,69
### Reasoning:
<|cot_start|>Examples:
  13,66 -> 1366
  45,48 -> 4548
  77,12 -> 7712
Check both candidate forms:
  concat(13,66)=1366  rev_concat(13,66)=6613  target=1366  concat
  concat(45,48)=4548  rev_concat(45,48)=4845  target=4548  concat
  concat(77,12)=7712  rev_concat(77,12)=1277  target=7712  concat
Conclude operator: concat.
Apply to (58, 69):  answer = 5869
Final: \boxed{5869}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00110000 -> 00011000
  11100011 -> 11110001
  10001010 -> 01000101
Apply to: 01111001
### Reasoning:
<|cot_start|>Given examples:
  00110000 -> 00011000
  11100011 -> 11110001
  10001010 -> 01000101
Compare each bit position across the three examples:
  bit 0: 0,1,1 -> 0,1,0
  bit 1: 0,1,0 -> 0,1,1
  bit 2: 1,1,0 -> 0,1,0
  bit 3: 1,0,0 -> 1,1,0
  bit 4: 0,0,1 -> 1,0,0
  bit 5: 0,0,0 -> 0,0,1
  bit 6: 0,1,1 -> 0,0,0
  bit 7: 0,1,0 -> 0,1,1
Deduce rule: rotate right 1.
Apply to 01111001:
  result = 10111100
Final: \boxed{10111100}


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


### Task: unit
### Problem:
Convert 25 days to hours.
### Reasoning:
<|cot_start|>Conversion factor: 1 days = 24 hours.
So 25 days = 25 * 24 hours.
Compute step by step:
  2 * 10^1 * 24 = 480
  running total = 480
  5 * 10^0 * 24 = 120
  running total = 600
Final: \boxed{600}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  38,70 -> 324
  11,76 -> 225
  86,60 -> 400
Apply to: 53,37
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  38,70: '+' gives 108; target=324  no
  38,70: '-' gives 32; target=324  no
  38,70: '*' gives 2660; target=324  no
  38,70: 'concat' gives 3870; target=324  no
  38,70: 'rev_concat' gives 7038; target=324  no
  38,70: 'max*min+sum' gives 2768; target=324  no
  38,70: 'digitsum2' gives 324; target=324  MATCH
  11,76: '+' gives 87; target=225  no
  11,76: '-' gives 65; target=225  no
  11,76: '*' gives 836; target=225  no
  11,76: 'concat' gives 1176; target=225  no
  11,76: 'rev_concat' gives 7611; target=225  no
  11,76: 'max*min+sum' gives 923; target=225  no
  11,76: 'digitsum2' gives 225; target=225  MATCH
  86,60: '+' gives 146; target=400  no
  86,60: '-' gives 26; target=400  no
  86,60: '*' gives 5160; target=400  no
  86,60: 'concat' gives 8660; target=400  no
  86,60: 'rev_concat' gives 6086; target=400  no
  86,60: 'max*min+sum' gives 5306; target=400  no
  86,60: 'digitsum2' gives 400; target=400  MATCH
The only operator consistent with all examples is 'digitsum2'.
Apply to (53, 37):
  result = 324
Final: \boxed{324}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  88,49 -> 4312
  71,28 -> 1988
  46,15 -> 690
Apply to: 62,98
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  88,49: '+' gives 137; target=4312  no
  88,49: '-' gives 39; target=4312  no
  88,49: '*' gives 4312; target=4312  MATCH
  88,49: 'concat' gives 8849; target=4312  no
  88,49: 'rev_concat' gives 4988; target=4312  no
  88,49: 'max*min+sum' gives 4449; target=4312  no
  88,49: 'digitsum2' gives 841; target=4312  no
  71,28: '+' gives 99; target=1988  no
  71,28: '-' gives 43; target=1988  no
  71,28: '*' gives 1988; target=1988  MATCH
  71,28: 'concat' gives 7128; target=1988  no
  71,28: 'rev_concat' gives 2871; target=1988  no
  71,28: 'max*min+sum' gives 2087; target=1988  no
  71,28: 'digitsum2' gives 324; target=1988  no
  46,15: '+' gives 61; target=690  no
  46,15: '-' gives 31; target=690  no
  46,15: '*' gives 690; target=690  MATCH
  46,15: 'concat' gives 4615; target=690  no
  46,15: 'rev_concat' gives 1546; target=690  no
  46,15: 'max*min+sum' gives 751; target=690  no
  46,15: 'digitsum2' gives 256; target=690  no
The only operator consistent with all examples is '*'.
Apply to (62, 98):
  result = 6076
Final: \boxed{6076}


### Task: numeral
### Problem:
Convert the Roman numeral LXII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  X = 10  ->  50 + 10 = 60
  I = 1  ->  60 + 1 = 61
  I = 1  ->  61 + 1 = 62
Final: \boxed{62}


### Task: gravity
### Problem:
A mass of 29 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 = 29 * 981.
Step-by-step multiplication:
  2 * 10^1 * 981 = 19620
  running total = 19620
  9 * 10^0 * 981 = 8829
  running total = 28449
So F = 28449 centiNewtons = 284.49 N.
Final: \boxed{284.49}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  00001111 -> 11110000
  01010001 -> 10101110
  10101000 -> 01010111
Apply to: 01011000
### Reasoning:
<|cot_start|>Given examples:
  00001111 -> 11110000
  01010001 -> 10101110
  10101000 -> 01010111
Compare each bit position across the three examples:
  bit 0: 0,0,1 -> 1,1,0
  bit 1: 0,1,0 -> 1,0,1
  bit 2: 0,0,1 -> 1,1,0
  bit 3: 0,1,0 -> 1,0,1
  bit 4: 1,0,1 -> 0,1,0
  bit 5: 1,0,0 -> 0,1,1
  bit 6: 1,0,0 -> 0,1,1
  bit 7: 1,1,0 -> 0,0,1
Deduce rule: invert (NOT).
Apply to 01011000:
  result = 10100111
Final: \boxed{10100111}


### Task: numeral
### Problem:
Convert the Roman numeral LVII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  L = 50  ->  0 + 50 = 50
  V = 5  ->  50 + 5 = 55
  I = 1  ->  55 + 1 = 56
  I = 1  ->  56 + 1 = 57
Final: \boxed{57}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  26,66 -> 92
  65,22 -> 87
  56,38 -> 94
Apply to: 25,51
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  26,66: '+' gives 92; target=92  MATCH
  26,66: '-' gives 40; target=92  no
  26,66: '*' gives 1716; target=92  no
  26,66: 'concat' gives 2666; target=92  no
  26,66: 'rev_concat' gives 6626; target=92  no
  26,66: 'max*min+sum' gives 1808; target=92  no
  26,66: 'digitsum2' gives 400; target=92  no
  65,22: '+' gives 87; target=87  MATCH
  65,22: '-' gives 43; target=87  no
  65,22: '*' gives 1430; target=87  no
  65,22: 'concat' gives 6522; target=87  no
  65,22: 'rev_concat' gives 2265; target=87  no
  65,22: 'max*min+sum' gives 1517; target=87  no
  65,22: 'digitsum2' gives 225; target=87  no
  56,38: '+' gives 94; target=94  MATCH
  56,38: '-' gives 18; target=94  no
  56,38: '*' gives 2128; target=94  no
  56,38: 'concat' gives 5638; target=94  no
  56,38: 'rev_concat' gives 3856; target=94  no
  56,38: 'max*min+sum' gives 2222; target=94  no
  56,38: 'digitsum2' gives 484; target=94  no
The only operator consistent with all examples is '+'.
Apply to (25, 51):
  result = 76
Final: \boxed{76}


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


### Task: numeral
### Problem:
Convert the Roman numeral XXXIII to an integer.
### Reasoning:
<|cot_start|>Reading symbols one by one:
  X = 10  ->  0 + 10 = 10
  X = 10  ->  10 + 10 = 20
  X = 10  ->  20 + 10 = 30
  I = 1  ->  30 + 1 = 31
  I = 1  ->  31 + 1 = 32
  I = 1  ->  32 + 1 = 33
Final: \boxed{33}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11000011 -> 11000011
  11100011 -> 11000111
  01101101 -> 10110110
Apply to: 10000001
### Reasoning:
<|cot_start|>Given examples:
  11000011 -> 11000011
  11100011 -> 11000111
  01101101 -> 10110110
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 1,1,1
  bit 1: 1,1,1 -> 1,1,0
  bit 2: 0,1,1 -> 0,0,1
  bit 3: 0,0,0 -> 0,0,1
  bit 4: 0,0,1 -> 0,0,0
  bit 5: 0,0,1 -> 0,1,1
  bit 6: 1,1,0 -> 1,1,1
  bit 7: 1,1,1 -> 1,1,0
Deduce rule: reverse bits.
Apply to 10000001:
  result = 10000001
Final: \boxed{10000001}


### Task: gravity
### Problem:
A mass of 16 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 = 16 * 981.
Step-by-step multiplication:
  1 * 10^1 * 981 = 9810
  running total = 9810
  6 * 10^0 * 981 = 5886
  running total = 15696
So F = 15696 centiNewtons = 156.96 N.
Final: \boxed{156.96}


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11111101 -> 11111101
  01001010 -> 11111010
  10000000 -> 11110000
Apply to: 10100100
### Reasoning:
<|cot_start|>Given examples:
  11111101 -> 11111101
  01001010 -> 11111010
  10000000 -> 11110000
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 1,1,1
  bit 1: 1,1,0 -> 1,1,1
  bit 2: 1,0,0 -> 1,1,1
  bit 3: 1,0,0 -> 1,1,1
  bit 4: 1,1,0 -> 1,1,0
  bit 5: 1,0,0 -> 1,0,0
  bit 6: 0,1,0 -> 0,1,0
  bit 7: 1,0,0 -> 1,0,0
Deduce rule: or 0xF0.
Apply to 10100100:
  result = 11110100
Final: \boxed{11110100}


### Task: gravity
### Problem:
A mass of 44 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 = 44 * 981.
Step-by-step multiplication:
  4 * 10^1 * 981 = 39240
  running total = 39240
  4 * 10^0 * 981 = 3924
  running total = 43164
So F = 43164 centiNewtons = 431.64 N.
Final: \boxed{431.64}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  14,99 -> 9914
  21,22 -> 2221
  85,27 -> 2785
Apply to: 28,82
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  14,99: '+' gives 113; target=9914  no
  14,99: '-' gives 85; target=9914  no
  14,99: '*' gives 1386; target=9914  no
  14,99: 'concat' gives 1499; target=9914  no
  14,99: 'rev_concat' gives 9914; target=9914  MATCH
  14,99: 'max*min+sum' gives 1499; target=9914  no
  14,99: 'digitsum2' gives 529; target=9914  no
  21,22: '+' gives 43; target=2221  no
  21,22: '-' gives 1; target=2221  no
  21,22: '*' gives 462; target=2221  no
  21,22: 'concat' gives 2122; target=2221  no
  21,22: 'rev_concat' gives 2221; target=2221  MATCH
  21,22: 'max*min+sum' gives 505; target=2221  no
  21,22: 'digitsum2' gives 49; target=2221  no
  85,27: '+' gives 112; target=2785  no
  85,27: '-' gives 58; target=2785  no
  85,27: '*' gives 2295; target=2785  no
  85,27: 'concat' gives 8527; target=2785  no
  85,27: 'rev_concat' gives 2785; target=2785  MATCH
  85,27: 'max*min+sum' gives 2407; target=2785  no
  85,27: 'digitsum2' gives 484; target=2785  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (28, 82):
  result = 8228
Final: \boxed{8228}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  79,25 -> 104
  50,13 -> 63
  65,28 -> 93
Apply to: 21,26
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  79,25: '+' gives 104; target=104  MATCH
  79,25: '-' gives 54; target=104  no
  79,25: '*' gives 1975; target=104  no
  79,25: 'concat' gives 7925; target=104  no
  79,25: 'rev_concat' gives 2579; target=104  no
  79,25: 'max*min+sum' gives 2079; target=104  no
  79,25: 'digitsum2' gives 529; target=104  no
  50,13: '+' gives 63; target=63  MATCH
  50,13: '-' gives 37; target=63  no
  50,13: '*' gives 650; target=63  no
  50,13: 'concat' gives 5013; target=63  no
  50,13: 'rev_concat' gives 1350; target=63  no
  50,13: 'max*min+sum' gives 713; target=63  no
  50,13: 'digitsum2' gives 81; target=63  no
  65,28: '+' gives 93; target=93  MATCH
  65,28: '-' gives 37; target=93  no
  65,28: '*' gives 1820; target=93  no
  65,28: 'concat' gives 6528; target=93  no
  65,28: 'rev_concat' gives 2865; target=93  no
  65,28: 'max*min+sum' gives 1913; target=93  no
  65,28: 'digitsum2' gives 441; target=93  no
The only operator consistent with all examples is '+'.
Apply to (21, 26):
  result = 47
Final: \boxed{47}


### 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: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  11100010 -> 00000010
  01011000 -> 00001000
  10110101 -> 00000101
Apply to: 11011010
### Reasoning:
<|cot_start|>Given examples:
  11100010 -> 00000010
  01011000 -> 00001000
  10110101 -> 00000101
Compare each bit position across the three examples:
  bit 0: 1,0,1 -> 0,0,0
  bit 1: 1,1,0 -> 0,0,0
  bit 2: 1,0,1 -> 0,0,0
  bit 3: 0,1,1 -> 0,0,0
  bit 4: 0,1,0 -> 0,1,0
  bit 5: 0,0,1 -> 0,0,1
  bit 6: 1,0,0 -> 1,0,0
  bit 7: 0,0,1 -> 0,0,1
Deduce rule: and 0x0F.
Apply to 11011010:
  result = 00001010
Final: \boxed{00001010}


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  53,39 -> 14
  40,35 -> 5
  34,97 -> 63
Apply to: 58,25
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  53,39: '+' gives 92; target=14  no
  53,39: '-' gives 14; target=14  MATCH
  53,39: '*' gives 2067; target=14  no
  53,39: 'concat' gives 5339; target=14  no
  53,39: 'rev_concat' gives 3953; target=14  no
  53,39: 'max*min+sum' gives 2159; target=14  no
  53,39: 'digitsum2' gives 400; target=14  no
  40,35: '+' gives 75; target=5  no
  40,35: '-' gives 5; target=5  MATCH
  40,35: '*' gives 1400; target=5  no
  40,35: 'concat' gives 4035; target=5  no
  40,35: 'rev_concat' gives 3540; target=5  no
  40,35: 'max*min+sum' gives 1475; target=5  no
  40,35: 'digitsum2' gives 144; target=5  no
  34,97: '+' gives 131; target=63  no
  34,97: '-' gives 63; target=63  MATCH
  34,97: '*' gives 3298; target=63  no
  34,97: 'concat' gives 3497; target=63  no
  34,97: 'rev_concat' gives 9734; target=63  no
  34,97: 'max*min+sum' gives 3429; target=63  no
  34,97: 'digitsum2' gives 529; target=63  no
The only operator consistent with all examples is '-'.
Apply to (58, 25):
  result = 33
Final: \boxed{33}


### Task: unit
### Problem:
Convert 48 kilometres to metres.
### Reasoning:
<|cot_start|>Conversion factor: 1 kilometres = 1000 metres.
So 48 kilometres = 48 * 1000 metres.
Compute step by step:
  4 * 10^1 * 1000 = 40000
  running total = 40000
  8 * 10^0 * 1000 = 8000
  running total = 48000
Final: \boxed{48000}


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


### Task: equation
### Problem:
Discover the operator from examples then apply it:
  64,48 -> 4864
  68,17 -> 1768
  27,54 -> 5427
Apply to: 32,73
### Reasoning:
<|cot_start|>Test candidate operators on the examples:
  64,48: '+' gives 112; target=4864  no
  64,48: '-' gives 16; target=4864  no
  64,48: '*' gives 3072; target=4864  no
  64,48: 'concat' gives 6448; target=4864  no
  64,48: 'rev_concat' gives 4864; target=4864  MATCH
  64,48: 'max*min+sum' gives 3184; target=4864  no
  64,48: 'digitsum2' gives 484; target=4864  no
  68,17: '+' gives 85; target=1768  no
  68,17: '-' gives 51; target=1768  no
  68,17: '*' gives 1156; target=1768  no
  68,17: 'concat' gives 6817; target=1768  no
  68,17: 'rev_concat' gives 1768; target=1768  MATCH
  68,17: 'max*min+sum' gives 1241; target=1768  no
  68,17: 'digitsum2' gives 484; target=1768  no
  27,54: '+' gives 81; target=5427  no
  27,54: '-' gives 27; target=5427  no
  27,54: '*' gives 1458; target=5427  no
  27,54: 'concat' gives 2754; target=5427  no
  27,54: 'rev_concat' gives 5427; target=5427  MATCH
  27,54: 'max*min+sum' gives 1539; target=5427  no
  27,54: 'digitsum2' gives 324; target=5427  no
The only operator consistent with all examples is 'rev_concat'.
Apply to (32, 73):
  result = 7332
Final: \boxed{7332}


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


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


### Task: unit
### Problem:
Convert 70 litres to millilitres.
### Reasoning:
<|cot_start|>Conversion factor: 1 litres = 1000 millilitres.
So 70 litres = 70 * 1000 millilitres.
Compute step by step:
  7 * 10^1 * 1000 = 70000
  running total = 70000
  0 * 10^0 * 1000 = 0
  running total = 70000
Final: \boxed{70000}


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


### Task: bit
### Problem:
Discover the 8-bit transformation rule from examples then apply it.
Examples:
  10001101 -> 00100111
  10000101 -> 00101111
  01000111 -> 11101101
Apply to: 00010100
### Reasoning:
<|cot_start|>Given examples:
  10001101 -> 00100111
  10000101 -> 00101111
  01000111 -> 11101101
Compare each bit position across the three examples:
  bit 0: 1,1,0 -> 0,0,1
  bit 1: 0,0,1 -> 0,0,1
  bit 2: 0,0,0 -> 1,1,1
  bit 3: 0,0,0 -> 0,0,0
  bit 4: 1,0,0 -> 0,1,1
  bit 5: 1,1,1 -> 1,1,1
  bit 6: 0,0,1 -> 1,1,0
  bit 7: 1,1,1 -> 1,1,1
Deduce rule: xor 0xAA.
Apply to 00010100:
  result = 10111110
Final: \boxed{10111110}


### 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: cryptarithm
### Problem:
Cryptarithm-style mapping.  Examples:
  68,69 -> 6869
  43,70 -> 4370
  22,20 -> 2220
Apply to: 97,32
### Reasoning:
<|cot_start|>Examples:
  68,69 -> 6869
  43,70 -> 4370
  22,20 -> 2220
Check both candidate forms:
  concat(68,69)=6869  rev_concat(68,69)=6968  target=6869  concat
  concat(43,70)=4370  rev_concat(43,70)=7043  target=4370  concat
  concat(22,20)=2220  rev_concat(22,20)=2022  target=2220  concat
Conclude operator: concat.
Apply to (97, 32):  answer = 9732
Final: \boxed{9732}


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