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: Luke, Alexander, Liam, Mason, Sophia, and Ava. Luke commented, "If Ava is a knight then Mason is a knave". Alexander remarked, "Ava is a knight if and only if Luke is a knight". In Liam's words: "Liam is a knight if and only if Ava is a knave". Mason stated, "Ava is not a knave". Sophia noted, "If Mason is a knave then Liam is a knave". According to Ava, "Sophia is not a knave". 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 Luke is a knight.  No contradiction is found in their claim that If Ava is a knight then Mason is a knave.
 Assume Ava is a knight.  No contradiction is found in their claim that Sophia is not a knave.
 Assume Sophia is a knight.  No contradiction is found in their claim that If Mason is a knave then Liam is a knave.
 Mason cannot be a knight, because this would contradict the claim of Luke that If Ava is a knight then Mason is a knave.
 Mason cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.
 We have exhausted all possibilities for Mason, so let us go back and reconsider Sophia.
 Sophia cannot be a knave, because this would contradict the claim of Ava that Sophia is not a knave.
 We have exhausted all possibilities for Sophia, so let us go back and reconsider Ava.
 Assume Ava is a knave.  No contradiction is found in their false claim that Sophia is not a knave.
 Sophia cannot be a knight, because this would contradict the false claim of Ava that Sophia is not a knave.
 Assume Sophia is a knave.  No contradiction is found in their false claim that If Mason is a knave then Liam is a knave.
 Mason cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.
 Assume Mason is a knave.  No contradiction is found in their false claim that Ava is not a knave.
 Assume Liam is a knight.  No contradiction is found in their claim that Liam is a knight if and only if Ava is a knave.
 Alexander cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Luke is a knight.
 Assume Alexander is a knave.  No contradiction is found in their false claim that Ava is a knight if and only if Luke is a knight.
 Therefore, (1) Luke is a knight
 (2) Alexander is a knave
 (3) Liam is a knight
 (4) Mason is a knave
 (5) Sophia is a knave
 (6) Ava 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: Luke, Alexander, Liam, Mason, Sophia, and Ava. Luke commented, "If Ava is a knight then Mason is a knave". Alexander remarked, "Ava is a knight if and only if Luke is a knight". In Liam's words: "Liam is a knight if and only if Ava is a knave". Mason stated, "Ava is not a knave". Sophia noted, "If Mason is a knave then Liam is a knave". According to Ava, "Sophia is not a knave". 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 Luke is a knight. No contradiction is found in their claim that If Ava is a knight then Mason is a knave.
Assume Ava is a knight. No contradiction is found in their claim that Sophia is not a knave.
Assume Sophia is a knight. No contradiction is found in their claim that If Mason is a knave then Liam is a knave.
Mason cannot be a knight, because this would contradict the claim of Luke that If Ava is a knight then Mason is a knave.
Mason cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.
We have exhausted all possibilities for Mason, so let us go back and reconsider Sophia.
Sophia cannot be a knave, because this would contradict the claim of Ava that Sophia is not a knave.
We have exhausted all possibilities for Sophia, so let us go back and reconsider Ava.
Assume Ava is a knave. No contradiction is found in their false claim that Sophia is not a knave.
Sophia cannot be a knight, because this would contradict the false claim of Ava that Sophia is not a knave.
Assume Sophia is a knave. No contradiction is found in their false claim that If Mason is a knave then Liam is a knave.
Mason cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.
Assume Mason is a knave. No contradiction is found in their false claim that Ava is not a knave.
Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight if and only if Ava is a knave.
Alexander cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Luke is a knight.
Assume Alexander is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Luke is a knight.
Therefore, (1) Luke is a knight
(2) Alexander is a knave
(3) Liam is a knight
(4) Mason is a knave
(5) Sophia is a knave
(6) Ava is a knave </think>
<answer> (1) Luke is a knight
(2) Alexander is a knave
(3) Liam is a knight
(4) Mason is a knave
(5) Sophia is a knave
(6) Ava is a knave </answer>
Luke Alexander Liam Mason Sophia Ava
(1) Luke is a knight
(2) Alexander is a knave
(3) Liam is a knight
(4) Mason is a knave
(5) Sophia is a knave
(6) Ava is a knave
(('->', ('telling-truth', 5), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('not', ('lying', 5)), ('->', ('lying', 3), ('lying', 2)), ('not', ('lying', 4)))
rule