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: Oliver, Aiden, Zoey, and Isabella. Oliver stated, "Isabella is a knight". Aiden noted, "Oliver is a knave or Zoey is a knight". Zoey asserted: "Oliver is a knave if and only if Aiden is a knight". In a statement by Isabella: "Zoey 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 Oliver is a knight.  No contradiction is found in their claim that Isabella is a knight.
 Assume Isabella is a knight.  No contradiction is found in their claim that Zoey is not a knight.
 Zoey cannot be a knight, because this would contradict the claim of Isabella that Zoey is not a knight.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Oliver is a knave if and only if Aiden is a knight.
 Aiden cannot be a knight, because this would contradict the claim of their own that Oliver is a knave or Zoey is a knight.
 Aiden cannot be a knave, because this would contradict the false claim of Zoey that Oliver is a knave if and only if Aiden is a knight.
 We have exhausted all possibilities for Aiden and Zoey, so let us go back and reconsider Isabella.
 Isabella cannot be a knave, because this would contradict the claim of Oliver that Isabella is a knight.
 We have exhausted all possibilities for Isabella, so let us go back and reconsider Oliver.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Isabella is a knight.
 Isabella cannot be a knight, because this would contradict the false claim of Oliver that Isabella is a knight.
 Assume Isabella is a knave.  No contradiction is found in their false claim that Zoey is not a knight.
 Assume Zoey is a knight.  No contradiction is found in their claim that Oliver is a knave if and only if Aiden is a knight.
 Assume Aiden is a knight.  No contradiction is found in their claim that Oliver is a knave or Zoey is a knight.
 Therefore, (1) Oliver is a knave
 (2) Aiden is a knight
 (3) Zoey is a knight
 (4) Isabella 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 4 inhabitants: Oliver, Aiden, Zoey, and Isabella. Oliver stated, "Isabella is a knight". Aiden noted, "Oliver is a knave or Zoey is a knight". Zoey asserted: "Oliver is a knave if and only if Aiden is a knight". In a statement by Isabella: "Zoey 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 Oliver is a knight. No contradiction is found in their claim that Isabella is a knight.
Assume Isabella is a knight. No contradiction is found in their claim that Zoey is not a knight.
Zoey cannot be a knight, because this would contradict the claim of Isabella that Zoey is not a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Aiden is a knight.
Aiden cannot be a knight, because this would contradict the claim of their own that Oliver is a knave or Zoey is a knight.
Aiden cannot be a knave, because this would contradict the false claim of Zoey that Oliver is a knave if and only if Aiden is a knight.
We have exhausted all possibilities for Aiden and Zoey, so let us go back and reconsider Isabella.
Isabella cannot be a knave, because this would contradict the claim of Oliver that Isabella is a knight.
We have exhausted all possibilities for Isabella, so let us go back and reconsider Oliver.
Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knight.
Isabella cannot be a knight, because this would contradict the false claim of Oliver that Isabella is a knight.
Assume Isabella is a knave. No contradiction is found in their false claim that Zoey is not a knight.
Assume Zoey is a knight. No contradiction is found in their claim that Oliver is a knave if and only if Aiden is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Oliver is a knave or Zoey is a knight.
Therefore, (1) Oliver is a knave
(2) Aiden is a knight
(3) Zoey is a knight
(4) Isabella is a knave </think>
<answer> (1) Oliver is a knave
(2) Aiden is a knight
(3) Zoey is a knight
(4) Isabella is a knave </answer>
Oliver Aiden Zoey Isabella
(1) Oliver is a knave
(2) Aiden is a knight
(3) Zoey is a knight
(4) Isabella is a knave
(('telling-truth', 3), ('or', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('not', ('telling-truth', 2)))
rule