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