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: Amelia, Penelope, and Evelyn. Amelia said that Evelyn is not a knight. Penelope was heard saying, "Penelope is a knight or Evelyn is a knave". Evelyn was heard saying, "Penelope is a knight if and only if Penelope is a knave". 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 Amelia is a knight.  No contradiction is found in their claim that Evelyn is not a knight.
 Evelyn cannot be a knight, because this would contradict the claim of Amelia that Evelyn is not a knight.
 Assume Evelyn is a knave.  No contradiction is found in their false claim that Penelope is a knight if and only if Penelope is a knave.
 Assume Penelope is a knight.  No contradiction is found in their claim that Penelope is a knight or Evelyn is a knave.
 Therefore, (1) Amelia is a knight
 (2) Penelope is a knight
 (3) Evelyn 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: Amelia, Penelope, and Evelyn. Amelia said that Evelyn is not a knight. Penelope was heard saying, "Penelope is a knight or Evelyn is a knave". Evelyn was heard saying, "Penelope is a knight if and only if Penelope is a knave". 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 Amelia is a knight. No contradiction is found in their claim that Evelyn is not a knight.
Evelyn cannot be a knight, because this would contradict the claim of Amelia that Evelyn is not a knight.
Assume Evelyn is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Penelope is a knave.
Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight or Evelyn is a knave.
Therefore, (1) Amelia is a knight
(2) Penelope is a knight
(3) Evelyn is a knave </think>
<answer> (1) Amelia is a knight
(2) Penelope is a knight
(3) Evelyn is a knave </answer>
Amelia Penelope Evelyn
(1) Amelia is a knight
(2) Penelope is a knight
(3) Evelyn is a knave
(('not', ('telling-truth', 2)), ('or', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))
rule