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 7 inhabitants: Michael, Joseph, Jackson, Aurora, Sebastian, Jacob, and Zoey. According to Michael, "If Aurora is a knight then Jackson is a knight". As Joseph put it, "Sebastian is a knight if and only if Sebastian is a knave". "Michael is a knave if and only if Jacob is a knave" - Jackson. Aurora was heard saying, "Michael is a knight". Sebastian said, "Zoey is a knight and Joseph is a knight." "Joseph is a knight if and only if Sebastian is a knight," Jacob declared. "If Sebastian is a knave then Aurora is a knave," Zoey declared. 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 If Aurora is a knight then Jackson is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Michael is a knight.
 Assume Jackson is a knight.  No contradiction is found in their claim that Michael is a knave if and only if Jacob is a knave.
 Assume Jacob is a knight.  No contradiction is found in their claim that Joseph is a knight if and only if Sebastian is a knight.
 Joseph cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Sebastian is a knave.
 Assume Joseph is a knave.  No contradiction is found in their false claim that Sebastian is a knight if and only if Sebastian is a knave.
 Sebastian cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Joseph is a knight.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Zoey is a knight and Joseph is a knight.
 Zoey cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knave then Aurora is a knave.
 Assume Zoey is a knave.  No contradiction is found in their false claim that If Sebastian is a knave then Aurora is a knave.
 Therefore, (1) Michael is a knight
 (2) Joseph is a knave
 (3) Jackson is a knight
 (4) Aurora is a knight
 (5) Sebastian is a knave
 (6) Jacob is a knight
 (7) Zoey 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 7 inhabitants: Michael, Joseph, Jackson, Aurora, Sebastian, Jacob, and Zoey. According to Michael, "If Aurora is a knight then Jackson is a knight". As Joseph put it, "Sebastian is a knight if and only if Sebastian is a knave". "Michael is a knave if and only if Jacob is a knave" - Jackson. Aurora was heard saying, "Michael is a knight". Sebastian said, "Zoey is a knight and Joseph is a knight." "Joseph is a knight if and only if Sebastian is a knight," Jacob declared. "If Sebastian is a knave then Aurora is a knave," Zoey declared. 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 If Aurora is a knight then Jackson is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knight.
Assume Jackson is a knight. No contradiction is found in their claim that Michael is a knave if and only if Jacob is a knave.
Assume Jacob is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Sebastian is a knight.
Joseph cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Sebastian is a knave.
Assume Joseph is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Sebastian is a knave.
Sebastian cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Joseph is a knight.
Assume Sebastian is a knave. No contradiction is found in their false claim that Zoey is a knight and Joseph is a knight.
Zoey cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knave then Aurora is a knave.
Assume Zoey is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Aurora is a knave.
Therefore, (1) Michael is a knight
(2) Joseph is a knave
(3) Jackson is a knight
(4) Aurora is a knight
(5) Sebastian is a knave
(6) Jacob is a knight
(7) Zoey is a knave </think>
<answer> (1) Michael is a knight
(2) Joseph is a knave
(3) Jackson is a knight
(4) Aurora is a knight
(5) Sebastian is a knave
(6) Jacob is a knight
(7) Zoey is a knave </answer>
Michael Joseph Jackson Aurora Sebastian Jacob Zoey
(1) Michael is a knight
(2) Joseph is a knave
(3) Jackson is a knight
(4) Aurora is a knight
(5) Sebastian is a knave
(6) Jacob is a knight
(7) Zoey is a knave
(('->', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 4)), ('<=>', ('lying', 0), ('lying', 5)), ('telling-truth', 0), ('and', ('telling-truth', 6), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 3)))
rule