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: Ava, Jackson, Alexander, and William. Ava remarked, "Alexander is a knave and Jackson is a knight". Jackson commented, "William is a knight". "Ava is a knave if and only if William is a knave" - Alexander. William remarked, "Alexander is a knight and Ava 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 Ava is a knight.  No contradiction is found in their claim that Alexander is a knave and Jackson is a knight.
 Alexander cannot be a knight, because this would contradict the claim of Ava that Alexander is a knave and Jackson is a knight.
 Assume Alexander is a knave.  No contradiction is found in their false claim that Ava is a knave if and only if William is a knave.
 William cannot be a knight, because this would contradict the false claim of Alexander that Ava is a knave if and only if William is a knave.
 Assume William is a knave.  No contradiction is found in their false claim that Alexander is a knight and Ava is a knight.
 Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight.
 Jackson cannot be a knave, because this would contradict the claim of Ava that Alexander is a knave and Jackson is a knight.
 We have exhausted all possibilities for Jackson, William, and Alexander, so let us go back and reconsider Ava.
 Assume Ava is a knave.  No contradiction is found in their false claim that Alexander is a knave and Jackson is a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that Ava is a knave if and only if William is a knave.
 William cannot be a knight, because this would contradict the claim of Alexander that Ava is a knave if and only if William is a knave.
 Assume William is a knave.  No contradiction is found in their false claim that Alexander is a knight and Ava is a knight.
 Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight.
 Assume Jackson is a knave.  No contradiction is found in their false claim that William is a knight.
 Therefore, (1) Ava is a knave
 (2) Jackson is a knave
 (3) Alexander is a knight
 (4) William 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: Ava, Jackson, Alexander, and William. Ava remarked, "Alexander is a knave and Jackson is a knight". Jackson commented, "William is a knight". "Ava is a knave if and only if William is a knave" - Alexander. William remarked, "Alexander is a knight and Ava 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 Ava is a knight. No contradiction is found in their claim that Alexander is a knave and Jackson is a knight.
Alexander cannot be a knight, because this would contradict the claim of Ava that Alexander is a knave and Jackson is a knight.
Assume Alexander is a knave. No contradiction is found in their false claim that Ava is a knave if and only if William is a knave.
William cannot be a knight, because this would contradict the false claim of Alexander that Ava is a knave if and only if William is a knave.
Assume William is a knave. No contradiction is found in their false claim that Alexander is a knight and Ava is a knight.
Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight.
Jackson cannot be a knave, because this would contradict the claim of Ava that Alexander is a knave and Jackson is a knight.
We have exhausted all possibilities for Jackson, William, and Alexander, so let us go back and reconsider Ava.
Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knave and Jackson is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Ava is a knave if and only if William is a knave.
William cannot be a knight, because this would contradict the claim of Alexander that Ava is a knave if and only if William is a knave.
Assume William is a knave. No contradiction is found in their false claim that Alexander is a knight and Ava is a knight.
Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight.
Assume Jackson is a knave. No contradiction is found in their false claim that William is a knight.
Therefore, (1) Ava is a knave
(2) Jackson is a knave
(3) Alexander is a knight
(4) William is a knave </think>
<answer> (1) Ava is a knave
(2) Jackson is a knave
(3) Alexander is a knight
(4) William is a knave </answer>
Ava Jackson Alexander William
(1) Ava is a knave
(2) Jackson is a knave
(3) Alexander is a knight
(4) William is a knave
(('and', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 3), ('<=>', ('lying', 0), ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 0)))
rule