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 4 inhabitants: Emily, Sebastian, Aurora, and Jack. "Sebastian is a knight," Emily mentioned. In a statement by Sebastian: "Aurora is a knave or Aurora is a knight". As Aurora put it, "Sebastian is a knave and Emily is a knight". "Emily is a knight," Jack mentioned. 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 Emily is a knight.  No contradiction is found in their claim that Sebastian is a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Aurora is a knave or Aurora is a knight.
 Aurora cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Emily is a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Sebastian is a knave and Emily is a knight.
 Assume Jack is a knight.  No contradiction is found in their claim that Emily is a knight.
 Therefore, (1) Emily is a knight
 (2) Sebastian is a knight
 (3) Aurora is a knave
 (4) Jack 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 4 inhabitants: Emily, Sebastian, Aurora, and Jack. "Sebastian is a knight," Emily mentioned. In a statement by Sebastian: "Aurora is a knave or Aurora is a knight". As Aurora put it, "Sebastian is a knave and Emily is a knight". "Emily is a knight," Jack mentioned. 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 Emily is a knight. No contradiction is found in their claim that Sebastian is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Aurora is a knave or Aurora is a knight.
Aurora cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Emily is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Sebastian is a knave and Emily is a knight.
Assume Jack is a knight. No contradiction is found in their claim that Emily is a knight.
Therefore, (1) Emily is a knight
(2) Sebastian is a knight
(3) Aurora is a knave
(4) Jack is a knight </think>
<answer> (1) Emily is a knight
(2) Sebastian is a knight
(3) Aurora is a knave
(4) Jack is a knight </answer>
Emily Sebastian Aurora Jack
(1) Emily is a knight
(2) Sebastian is a knight
(3) Aurora is a knave
(4) Jack is a knight
(('telling-truth', 1), ('or', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 0)), ('telling-truth', 0))
rule