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 5 inhabitants: Mason, Ava, Sophia, Liam, and Aurora. "Liam is a knight," Mason mentioned. Ava was heard saying, "Mason is a knight if and only if Liam is a knave". Sophia commented, "If Ava is a knight then Sophia is a knight". Liam remarked, "Liam is a knight and Ava is a knight". In Aurora's words: "Mason is a knight". 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 Mason is a knight.  No contradiction is found in their claim that Liam is a knight.
 Assume Liam is a knight.  No contradiction is found in their claim that Liam is a knight and Ava is a knight.
 Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Liam is a knave.
 Ava cannot be a knave, because this would contradict the claim of Liam that Liam is a knight and Ava is a knight.
 We have exhausted all possibilities for Ava, so let us go back and reconsider Liam.
 Liam cannot be a knave, because this would contradict the claim of Mason that Liam is a knight.
 We have exhausted all possibilities for Liam, so let us go back and reconsider Mason.
 Assume Mason is a knave.  No contradiction is found in their false claim that Liam is a knight.
 Liam cannot be a knight, because this would contradict the false claim of Mason that Liam is a knight.
 Assume Liam is a knave.  No contradiction is found in their false claim that Liam is a knight and Ava is a knight.
 Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Liam is a knave.
 Assume Ava is a knave.  No contradiction is found in their false claim that Mason is a knight if and only if Liam is a knave.
 Assume Sophia is a knight.  No contradiction is found in their claim that If Ava is a knight then Sophia is a knight.
 Aurora cannot be a knight, because this would contradict the claim of their own that Mason is a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Mason is a knight.
 Therefore, (1) Mason is a knave
 (2) Ava is a knave
 (3) Sophia is a knight
 (4) Liam is a knave
 (5) Aurora is a knave
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 5 inhabitants: Mason, Ava, Sophia, Liam, and Aurora. "Liam is a knight," Mason mentioned. Ava was heard saying, "Mason is a knight if and only if Liam is a knave". Sophia commented, "If Ava is a knight then Sophia is a knight". Liam remarked, "Liam is a knight and Ava is a knight". In Aurora's words: "Mason is a knight". 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 Mason is a knight. No contradiction is found in their claim that Liam is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight and Ava is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Liam is a knave.
Ava cannot be a knave, because this would contradict the claim of Liam that Liam is a knight and Ava is a knight.
We have exhausted all possibilities for Ava, so let us go back and reconsider Liam.
Liam cannot be a knave, because this would contradict the claim of Mason that Liam is a knight.
We have exhausted all possibilities for Liam, so let us go back and reconsider Mason.
Assume Mason is a knave. No contradiction is found in their false claim that Liam is a knight.
Liam cannot be a knight, because this would contradict the false claim of Mason that Liam is a knight.
Assume Liam is a knave. No contradiction is found in their false claim that Liam is a knight and Ava is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Liam is a knave.
Assume Ava is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Liam is a knave.
Assume Sophia is a knight. No contradiction is found in their claim that If Ava is a knight then Sophia is a knight.
Aurora cannot be a knight, because this would contradict the claim of their own that Mason is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Mason is a knight.
Therefore, (1) Mason is a knave
(2) Ava is a knave
(3) Sophia is a knight
(4) Liam is a knave
(5) Aurora is a knave </think>
<answer> (1) Mason is a knave
(2) Ava is a knave
(3) Sophia is a knight
(4) Liam is a knave
(5) Aurora is a knave </answer>
Mason Ava Sophia Liam Aurora
(1) Mason is a knave
(2) Ava is a knave
(3) Sophia is a knight
(4) Liam is a knave
(5) Aurora is a knave
(('telling-truth', 3), ('<=>', ('telling-truth', 0), ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('telling-truth', 0))
rule