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 3 inhabitants: Luke, Aiden, and Mason. "Aiden is a knave and Mason is a knave," Luke declared. Aiden expressed that Aiden is a knight. "If Luke is a knave then Luke is a knight," Mason declared. 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 Luke is a knight.  No contradiction is found in their claim that Aiden is a knave and Mason is a knave.
 Aiden cannot be a knight, because this would contradict the claim of Luke that Aiden is a knave and Mason is a knave.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Aiden is a knight.
 Mason cannot be a knight, because this would contradict the claim of Luke that Aiden is a knave and Mason is a knave.
 Mason cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Luke is a knight.
 We have exhausted all possibilities for Mason and Aiden, so let us go back and reconsider Luke.
 Assume Luke is a knave.  No contradiction is found in their false claim that Aiden is a knave and Mason is a knave.
 Assume Aiden is a knight.  No contradiction is found in their claim that Aiden is a knight.
 Mason cannot be a knight, because this would contradict the claim of their own that If Luke is a knave then Luke is a knight.
 Assume Mason is a knave.  No contradiction is found in their false claim that If Luke is a knave then Luke is a knight.
 Therefore, (1) Luke is a knave
 (2) Aiden is a knight
 (3) Mason 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 3 inhabitants: Luke, Aiden, and Mason. "Aiden is a knave and Mason is a knave," Luke declared. Aiden expressed that Aiden is a knight. "If Luke is a knave then Luke is a knight," Mason declared. 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 Luke is a knight. No contradiction is found in their claim that Aiden is a knave and Mason is a knave.
Aiden cannot be a knight, because this would contradict the claim of Luke that Aiden is a knave and Mason is a knave.
Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight.
Mason cannot be a knight, because this would contradict the claim of Luke that Aiden is a knave and Mason is a knave.
Mason cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Luke is a knight.
We have exhausted all possibilities for Mason and Aiden, so let us go back and reconsider Luke.
Assume Luke is a knave. No contradiction is found in their false claim that Aiden is a knave and Mason is a knave.
Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight.
Mason cannot be a knight, because this would contradict the claim of their own that If Luke is a knave then Luke is a knight.
Assume Mason is a knave. No contradiction is found in their false claim that If Luke is a knave then Luke is a knight.
Therefore, (1) Luke is a knave
(2) Aiden is a knight
(3) Mason is a knave </think>
<answer> (1) Luke is a knave
(2) Aiden is a knight
(3) Mason is a knave </answer>
Luke Aiden Mason
(1) Luke is a knave
(2) Aiden is a knight
(3) Mason is a knave
(('and', ('lying', 1), ('lying', 2)), ('telling-truth', 1), ('->', ('lying', 0), ('telling-truth', 0)))
rule