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 5 inhabitants: Amelia, Avery, Owen, Henry, and Aurora. In Amelia's words: "Aurora is a knave". According to Avery, "Amelia is a knave and Avery is a knight". Owen expressed that Avery is a knave and Aurora is a knight. "If Owen is a knight then Avery is a knave," Henry declared. In Aurora's words: "Avery is not 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 Amelia is a knight.  No contradiction is found in their claim that Aurora is a knave.
 Aurora cannot be a knight, because this would contradict the claim of Amelia that Aurora is a knave.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Avery is not a knight.
 Avery cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Avery is a knight.
 Avery cannot be a knave, because this would contradict the false claim of Aurora that Avery is not a knight.
 We have exhausted all possibilities for Avery and Aurora, so let us go back and reconsider Amelia.
 Assume Amelia is a knave.  No contradiction is found in their false claim that Aurora is a knave.
 Assume Aurora is a knight.  No contradiction is found in their claim that Avery is not a knight.
 Avery cannot be a knight, because this would contradict the claim of Aurora that Avery is not a knight.
 Assume Avery is a knave.  No contradiction is found in their false claim that Amelia is a knave and Avery is a knight.
 Assume Owen is a knight.  No contradiction is found in their claim that Avery is a knave and Aurora is a knight.
 Assume Henry is a knight.  No contradiction is found in their claim that If Owen is a knight then Avery is a knave.
 Therefore, (1) Amelia is a knave
 (2) Avery is a knave
 (3) Owen is a knight
 (4) Henry is a knight
 (5) Aurora 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 5 inhabitants: Amelia, Avery, Owen, Henry, and Aurora. In Amelia's words: "Aurora is a knave". According to Avery, "Amelia is a knave and Avery is a knight". Owen expressed that Avery is a knave and Aurora is a knight. "If Owen is a knight then Avery is a knave," Henry declared. In Aurora's words: "Avery is not 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 Amelia is a knight. No contradiction is found in their claim that Aurora is a knave.
Aurora cannot be a knight, because this would contradict the claim of Amelia that Aurora is a knave.
Assume Aurora is a knave. No contradiction is found in their false claim that Avery is not a knight.
Avery cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Avery is a knight.
Avery cannot be a knave, because this would contradict the false claim of Aurora that Avery is not a knight.
We have exhausted all possibilities for Avery and Aurora, so let us go back and reconsider Amelia.
Assume Amelia is a knave. No contradiction is found in their false claim that Aurora is a knave.
Assume Aurora is a knight. No contradiction is found in their claim that Avery is not a knight.
Avery cannot be a knight, because this would contradict the claim of Aurora that Avery is not a knight.
Assume Avery is a knave. No contradiction is found in their false claim that Amelia is a knave and Avery is a knight.
Assume Owen is a knight. No contradiction is found in their claim that Avery is a knave and Aurora is a knight.
Assume Henry is a knight. No contradiction is found in their claim that If Owen is a knight then Avery is a knave.
Therefore, (1) Amelia is a knave
(2) Avery is a knave
(3) Owen is a knight
(4) Henry is a knight
(5) Aurora is a knight </think>
<answer> (1) Amelia is a knave
(2) Avery is a knave
(3) Owen is a knight
(4) Henry is a knight
(5) Aurora is a knight </answer>
Amelia Avery Owen Henry Aurora
(1) Amelia is a knave
(2) Avery is a knave
(3) Owen is a knight
(4) Henry is a knight
(5) Aurora is a knight
(('lying', 4), ('and', ('lying', 0), ('telling-truth', 1)), ('and', ('lying', 1), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 1)))
rule