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: Penelope, Oliver, and Chloe. Penelope expressed that Chloe is a knight. According to Oliver, "Penelope is a knight". Chloe stated, "Chloe is a knight if and only if Oliver 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 Penelope is a knight.  No contradiction is found in their claim that Chloe is a knight.
 Assume Chloe is a knight.  No contradiction is found in their claim that Chloe is a knight if and only if Oliver is a knight.
 Assume Oliver is a knight.  No contradiction is found in their claim that Penelope is a knight.
 Therefore, (1) Penelope is a knight
 (2) Oliver is a knight
 (3) Chloe 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: Penelope, Oliver, and Chloe. Penelope expressed that Chloe is a knight. According to Oliver, "Penelope is a knight". Chloe stated, "Chloe is a knight if and only if Oliver 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 Penelope is a knight. No contradiction is found in their claim that Chloe is a knight.
Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Oliver is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Penelope is a knight.
Therefore, (1) Penelope is a knight
(2) Oliver is a knight
(3) Chloe is a knight </think>
<answer> (1) Penelope is a knight
(2) Oliver is a knight
(3) Chloe is a knight </answer>
Penelope Oliver Chloe
(1) Penelope is a knight
(2) Oliver is a knight
(3) Chloe is a knight
(('telling-truth', 2), ('telling-truth', 0), ('<=>', ('telling-truth', 2), ('telling-truth', 1)))
rule