A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Aria, Sofia, Amelia, James, and Jack. "Aria is a knight if and only if Sofia is a knight," William mentioned. Aria noted, "Sofia is a knave and Jack is a knight". "William is a knight or William is a knave," Sofia mentioned. Amelia commented, "James is a knave and James is a knight". In James's words: "William is a knight". Jack said, "William is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
user
Assume William is a knight.  No contradiction is found in their claim that Aria is a knight if and only if Sofia is a knight.
 Assume Aria is a knight.  No contradiction is found in their claim that Sofia is a knave and Jack is a knight.
 Sofia cannot be a knight, because this would contradict the claim of Aria that Sofia is a knave and Jack is a knight.
 Sofia cannot be a knave, because this would contradict the claim of William that Aria is a knight if and only if Sofia is a knight.
 We have exhausted all possibilities for Sofia, so let us go back and reconsider Aria.
 Assume Aria is a knave.  No contradiction is found in their false claim that Sofia is a knave and Jack is a knight.
 Sofia cannot be a knight, because this would contradict the claim of William that Aria is a knight if and only if Sofia is a knight.
 Sofia cannot be a knave, because this would contradict the false claim of their own that William is a knight or William is a knave.
 We have exhausted all possibilities for Sofia and Aria, so let us go back and reconsider William.
 Assume William is a knave.  No contradiction is found in their false claim that Aria is a knight if and only if Sofia is a knight.
 Assume Aria is a knight.  No contradiction is found in their claim that Sofia is a knave and Jack is a knight.
 Sofia cannot be a knight, because this would contradict the false claim of William that Aria is a knight if and only if Sofia is a knight.
 Sofia cannot be a knave, because this would contradict the false claim of their own that William is a knight or William is a knave.
 We have exhausted all possibilities for Sofia, so let us go back and reconsider Aria.
 Assume Aria is a knave.  No contradiction is found in their false claim that Sofia is a knave and Jack is a knight.
 Assume Sofia is a knight.  No contradiction is found in their claim that William is a knight or William is a knave.
 Assume Jack is a knight.  No contradiction is found in their claim that William is a knave.
 Amelia cannot be a knight, because this would contradict the claim of their own that James is a knave and James is a knight.
 Assume Amelia is a knave.  No contradiction is found in their false claim that James is a knave and James is a knight.
 James cannot be a knight, because this would contradict the claim of their own that William is a knight.
 Assume James is a knave.  No contradiction is found in their false claim that William is a knight.
 Therefore, (1) William is a knave
 (2) Aria is a knave
 (3) Sofia is a knight
 (4) Amelia is a knave
 (5) James is a knave
 (6) Jack is a knight
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Aria, Sofia, Amelia, James, and Jack. "Aria is a knight if and only if Sofia is a knight," William mentioned. Aria noted, "Sofia is a knave and Jack is a knight". "William is a knight or William is a knave," Sofia mentioned. Amelia commented, "James is a knave and James is a knight". In James's words: "William is a knight". Jack said, "William is a knave." So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
Assume William is a knight. No contradiction is found in their claim that Aria is a knight if and only if Sofia is a knight.
Assume Aria is a knight. No contradiction is found in their claim that Sofia is a knave and Jack is a knight.
Sofia cannot be a knight, because this would contradict the claim of Aria that Sofia is a knave and Jack is a knight.
Sofia cannot be a knave, because this would contradict the claim of William that Aria is a knight if and only if Sofia is a knight.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Aria.
Assume Aria is a knave. No contradiction is found in their false claim that Sofia is a knave and Jack is a knight.
Sofia cannot be a knight, because this would contradict the claim of William that Aria is a knight if and only if Sofia is a knight.
Sofia cannot be a knave, because this would contradict the false claim of their own that William is a knight or William is a knave.
We have exhausted all possibilities for Sofia and Aria, so let us go back and reconsider William.
Assume William is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Sofia is a knight.
Assume Aria is a knight. No contradiction is found in their claim that Sofia is a knave and Jack is a knight.
Sofia cannot be a knight, because this would contradict the false claim of William that Aria is a knight if and only if Sofia is a knight.
Sofia cannot be a knave, because this would contradict the false claim of their own that William is a knight or William is a knave.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Aria.
Assume Aria is a knave. No contradiction is found in their false claim that Sofia is a knave and Jack is a knight.
Assume Sofia is a knight. No contradiction is found in their claim that William is a knight or William is a knave.
Assume Jack is a knight. No contradiction is found in their claim that William is a knave.
Amelia cannot be a knight, because this would contradict the claim of their own that James is a knave and James is a knight.
Assume Amelia is a knave. No contradiction is found in their false claim that James is a knave and James is a knight.
James cannot be a knight, because this would contradict the claim of their own that William is a knight.
Assume James is a knave. No contradiction is found in their false claim that William is a knight.
Therefore, (1) William is a knave
(2) Aria is a knave
(3) Sofia is a knight
(4) Amelia is a knave
(5) James is a knave
(6) Jack is a knight </think>
<answer> (1) William is a knave
(2) Aria is a knave
(3) Sofia is a knight
(4) Amelia is a knave
(5) James is a knave
(6) Jack is a knight </answer>
William Aria Sofia Amelia James Jack
(1) William is a knave
(2) Aria is a knave
(3) Sofia is a knight
(4) Amelia is a knave
(5) James is a knave
(6) Jack is a knight
(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 0)), ('and', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 0), ('lying', 0))
rule