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