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: Aiden, Amelia, James, and William. According to Aiden, "James is a knave if and only if Amelia is a knave". Amelia told you that Aiden is a knave or Aiden is a knight. James asserted: "James is a knight or William is a knight". William expressed that Aiden is a knave or Aiden is 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 Aiden is a knight.  No contradiction is found in their claim that James is a knave if and only if Amelia is a knave.
 Assume James is a knight.  No contradiction is found in their claim that James is a knight or William is a knight.
 Assume William is a knight.  No contradiction is found in their claim that Aiden is a knave or Aiden is a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that Aiden is a knave or Aiden is a knight.
 Therefore, (1) Aiden is a knight
 (2) Amelia is a knight
 (3) James is a knight
 (4) William 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: Aiden, Amelia, James, and William. According to Aiden, "James is a knave if and only if Amelia is a knave". Amelia told you that Aiden is a knave or Aiden is a knight. James asserted: "James is a knight or William is a knight". William expressed that Aiden is a knave or Aiden is 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 Aiden is a knight. No contradiction is found in their claim that James is a knave if and only if Amelia is a knave.
Assume James is a knight. No contradiction is found in their claim that James is a knight or William is a knight.
Assume William is a knight. No contradiction is found in their claim that Aiden is a knave or Aiden is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Aiden is a knave or Aiden is a knight.
Therefore, (1) Aiden is a knight
(2) Amelia is a knight
(3) James is a knight
(4) William is a knight </think>
<answer> (1) Aiden is a knight
(2) Amelia is a knight
(3) James is a knight
(4) William is a knight </answer>
Aiden Amelia James William
(1) Aiden is a knight
(2) Amelia is a knight
(3) James is a knight
(4) William is a knight
(('<=>', ('lying', 2), ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('or', ('lying', 0), ('telling-truth', 0)))
rule