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 6 inhabitants: Michael, Sebastian, Evelyn, Isabella, Penelope, and Samuel. Michael was heard saying, "Penelope is not a knave". In Sebastian's words: "Isabella is a knight if and only if Isabella is a knave". In a statement by Evelyn: "Samuel is not a knave". "Penelope is a knave," Isabella declared. In Penelope's words: "Sebastian is a knave if and only if Penelope is a knight". Samuel noted, "Evelyn is a knave and Michael 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 Michael is a knight.  No contradiction is found in their claim that Penelope is not a knave.
 Assume Penelope is a knight.  No contradiction is found in their claim that Sebastian is a knave if and only if Penelope is a knight.
 Sebastian cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Isabella is a knave.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Isabella is a knight if and only if Isabella is a knave.
 Isabella cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.
 Assume Isabella is a knave.  No contradiction is found in their false claim that Penelope is a knave.
 Assume Evelyn is a knight.  No contradiction is found in their claim that Samuel is not a knave.
 Samuel cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Michael is a knave.
 Samuel cannot be a knave, because this would contradict the claim of Evelyn that Samuel is not a knave.
 We have exhausted all possibilities for Samuel, so let us go back and reconsider Evelyn.
 Assume Evelyn is a knave.  No contradiction is found in their false claim that Samuel is not a knave.
 Samuel cannot be a knight, because this would contradict the false claim of Evelyn that Samuel is not a knave.
 Assume Samuel is a knave.  No contradiction is found in their false claim that Evelyn is a knave and Michael is a knave.
 Therefore, (1) Michael is a knight
 (2) Sebastian is a knave
 (3) Evelyn is a knave
 (4) Isabella is a knave
 (5) Penelope is a knight
 (6) Samuel 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 6 inhabitants: Michael, Sebastian, Evelyn, Isabella, Penelope, and Samuel. Michael was heard saying, "Penelope is not a knave". In Sebastian's words: "Isabella is a knight if and only if Isabella is a knave". In a statement by Evelyn: "Samuel is not a knave". "Penelope is a knave," Isabella declared. In Penelope's words: "Sebastian is a knave if and only if Penelope is a knight". Samuel noted, "Evelyn is a knave and Michael 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 Michael is a knight. No contradiction is found in their claim that Penelope is not a knave.
Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Penelope is a knight.
Sebastian cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Isabella is a knave.
Assume Sebastian is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Isabella is a knave.
Isabella cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.
Assume Isabella is a knave. No contradiction is found in their false claim that Penelope is a knave.
Assume Evelyn is a knight. No contradiction is found in their claim that Samuel is not a knave.
Samuel cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Michael is a knave.
Samuel cannot be a knave, because this would contradict the claim of Evelyn that Samuel is not a knave.
We have exhausted all possibilities for Samuel, so let us go back and reconsider Evelyn.
Assume Evelyn is a knave. No contradiction is found in their false claim that Samuel is not a knave.
Samuel cannot be a knight, because this would contradict the false claim of Evelyn that Samuel is not a knave.
Assume Samuel is a knave. No contradiction is found in their false claim that Evelyn is a knave and Michael is a knave.
Therefore, (1) Michael is a knight
(2) Sebastian is a knave
(3) Evelyn is a knave
(4) Isabella is a knave
(5) Penelope is a knight
(6) Samuel is a knave </think>
<answer> (1) Michael is a knight
(2) Sebastian is a knave
(3) Evelyn is a knave
(4) Isabella is a knave
(5) Penelope is a knight
(6) Samuel is a knave </answer>
Michael Sebastian Evelyn Isabella Penelope Samuel
(1) Michael is a knight
(2) Sebastian is a knave
(3) Evelyn is a knave
(4) Isabella is a knave
(5) Penelope is a knight
(6) Samuel is a knave
(('not', ('lying', 4)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('not', ('lying', 5)), ('lying', 4), ('<=>', ('lying', 1), ('telling-truth', 4)), ('and', ('lying', 2), ('lying', 0)))
rule