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: James, Isabella, Aiden, Sofia, Matthew, and Aurora. James was heard saying, "Aiden is a knave if and only if Matthew is a knight". Isabella remarked, "Aurora is a knave and James is a knave". As Aiden put it, "Aurora is a knight or Aiden is a knight". Sofia said, "Matthew is a knave or James is a knave." Matthew stated, "James is a knave and Sofia is a knave". "Aurora is a knight if and only if James is a knave" - Aurora. 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 James is a knight.  No contradiction is found in their claim that Aiden is a knave if and only if Matthew is a knight.
 Assume Aiden is a knight.  No contradiction is found in their claim that Aurora is a knight or Aiden is a knight.
 Aurora cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if James is a knave.
 Aurora cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if James is a knave.
 We have exhausted all possibilities for Aurora, so let us go back and reconsider Aiden.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Aurora is a knight or Aiden is a knight.
 Aurora cannot be a knight, because this would contradict the false claim of Aiden that Aurora is a knight or Aiden is a knight.
 Aurora cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if James is a knave.
 We have exhausted all possibilities for Aurora and Aiden, so let us go back and reconsider James.
 Assume James is a knave.  No contradiction is found in their false claim that Aiden is a knave if and only if Matthew is a knight.
 Assume Aiden is a knight.  No contradiction is found in their claim that Aurora is a knight or Aiden is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Aurora is a knight if and only if James is a knave.
 Assume Matthew is a knight.  No contradiction is found in their claim that James is a knave and Sofia is a knave.
 Sofia cannot be a knight, because this would contradict the claim of Matthew that James is a knave and Sofia is a knave.
 Sofia cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or James is a knave.
 We have exhausted all possibilities for Sofia, so let us go back and reconsider Matthew.
 Matthew cannot be a knave, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.
 We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Aurora is a knight if and only if James is a knave.
 Assume Matthew is a knight.  No contradiction is found in their claim that James is a knave and Sofia is a knave.
 Sofia cannot be a knight, because this would contradict the claim of Matthew that James is a knave and Sofia is a knave.
 Sofia cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or James is a knave.
 We have exhausted all possibilities for Sofia, so let us go back and reconsider Matthew.
 Matthew cannot be a knave, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.
 We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Aiden.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Aurora is a knight or Aiden is a knight.
 Aurora cannot be a knight, because this would contradict the false claim of Aiden that Aurora is a knight or Aiden is a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Aurora is a knight if and only if James is a knave.
 Matthew cannot be a knight, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.
 Assume Matthew is a knave.  No contradiction is found in their false claim that James is a knave and Sofia is a knave.
 Assume Sofia is a knight.  No contradiction is found in their claim that Matthew is a knave or James is a knave.
 Assume Isabella is a knight.  No contradiction is found in their claim that Aurora is a knave and James is a knave.
 Therefore, (1) James is a knave
 (2) Isabella is a knight
 (3) Aiden is a knave
 (4) Sofia is a knight
 (5) Matthew is a knave
 (6) Aurora 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: James, Isabella, Aiden, Sofia, Matthew, and Aurora. James was heard saying, "Aiden is a knave if and only if Matthew is a knight". Isabella remarked, "Aurora is a knave and James is a knave". As Aiden put it, "Aurora is a knight or Aiden is a knight". Sofia said, "Matthew is a knave or James is a knave." Matthew stated, "James is a knave and Sofia is a knave". "Aurora is a knight if and only if James is a knave" - Aurora. 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 James is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Matthew is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Aurora is a knight or Aiden is a knight.
Aurora cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if James is a knave.
Aurora cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if James is a knave.
We have exhausted all possibilities for Aurora, so let us go back and reconsider Aiden.
Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knight or Aiden is a knight.
Aurora cannot be a knight, because this would contradict the false claim of Aiden that Aurora is a knight or Aiden is a knight.
Aurora cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if James is a knave.
We have exhausted all possibilities for Aurora and Aiden, so let us go back and reconsider James.
Assume James is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Matthew is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Aurora is a knight or Aiden is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight if and only if James is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that James is a knave and Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of Matthew that James is a knave and Sofia is a knave.
Sofia cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or James is a knave.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Matthew.
Matthew cannot be a knave, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.
Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if James is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that James is a knave and Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of Matthew that James is a knave and Sofia is a knave.
Sofia cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or James is a knave.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Matthew.
Matthew cannot be a knave, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.
We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Aiden.
Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knight or Aiden is a knight.
Aurora cannot be a knight, because this would contradict the false claim of Aiden that Aurora is a knight or Aiden is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if James is a knave.
Matthew cannot be a knight, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that James is a knave and Sofia is a knave.
Assume Sofia is a knight. No contradiction is found in their claim that Matthew is a knave or James is a knave.
Assume Isabella is a knight. No contradiction is found in their claim that Aurora is a knave and James is a knave.
Therefore, (1) James is a knave
(2) Isabella is a knight
(3) Aiden is a knave
(4) Sofia is a knight
(5) Matthew is a knave
(6) Aurora is a knave </think>
<answer> (1) James is a knave
(2) Isabella is a knight
(3) Aiden is a knave
(4) Sofia is a knight
(5) Matthew is a knave
(6) Aurora is a knave </answer>
James Isabella Aiden Sofia Matthew Aurora
(1) James is a knave
(2) Isabella is a knight
(3) Aiden is a knave
(4) Sofia is a knight
(5) Matthew is a knave
(6) Aurora is a knave
(('<=>', ('lying', 2), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 4), ('lying', 0)), ('and', ('lying', 0), ('lying', 3)), ('<=>', ('telling-truth', 5), ('lying', 0)))
rule