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: Lily, Matthew, and Riley. In a statement by Lily: "Lily is a knight if and only if Riley is a knight". "Lily is a knave," Matthew claimed. According to Riley, "Lily is a knave if and only if Riley 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 Lily is a knight.  No contradiction is found in their claim that Lily is a knight if and only if Riley is a knight.
 Riley cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Riley is a knight.
 Riley cannot be a knave, because this would contradict the claim of Lily that Lily is a knight if and only if Riley is a knight.
 We have exhausted all possibilities for Riley, so let us go back and reconsider Lily.
 Assume Lily is a knave.  No contradiction is found in their false claim that Lily is a knight if and only if Riley is a knight.
 Assume Riley is a knight.  No contradiction is found in their claim that Lily is a knave if and only if Riley is a knight.
 Assume Matthew is a knight.  No contradiction is found in their claim that Lily is a knave.
 Therefore, (1) Lily is a knave
 (2) Matthew is a knight
 (3) Riley 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 3 inhabitants: Lily, Matthew, and Riley. In a statement by Lily: "Lily is a knight if and only if Riley is a knight". "Lily is a knave," Matthew claimed. According to Riley, "Lily is a knave if and only if Riley 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 Lily is a knight. No contradiction is found in their claim that Lily is a knight if and only if Riley is a knight.
Riley cannot be a knight, because this would contradict the claim of their own that Lily is a knave if and only if Riley is a knight.
Riley cannot be a knave, because this would contradict the claim of Lily that Lily is a knight if and only if Riley is a knight.
We have exhausted all possibilities for Riley, so let us go back and reconsider Lily.
Assume Lily is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Riley is a knight.
Assume Riley is a knight. No contradiction is found in their claim that Lily is a knave if and only if Riley is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Lily is a knave.
Therefore, (1) Lily is a knave
(2) Matthew is a knight
(3) Riley is a knight </think>
<answer> (1) Lily is a knave
(2) Matthew is a knight
(3) Riley is a knight </answer>
Lily Matthew Riley
(1) Lily is a knave
(2) Matthew is a knight
(3) Riley is a knight
(('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 0), ('<=>', ('lying', 0), ('telling-truth', 2)))
rule