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 7 inhabitants: Harper, Ethan, Grace, Aurora, Ava, Mason, and Jackson. Harper remarked, "Ethan is a knave if and only if Aurora is a knight". Ethan said, "If Harper is a knight then Grace is a knave." In a statement by Grace: "Harper is a knight and Grace is a knight". "If Mason is a knight then Mason is a knave" - Aurora. According to Ava, "Grace is a knight if and only if Ava is a knight". Mason said that Harper is a knave if and only if Ava is a knave. Jackson remarked, "Mason is a knight or Harper is 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 Harper is a knight.  No contradiction is found in their claim that Ethan is a knave if and only if Aurora is a knight.
 Assume Ethan is a knight.  No contradiction is found in their claim that If Harper is a knight then Grace is a knave.
 Grace cannot be a knight, because this would contradict the claim of Ethan that If Harper is a knight then Grace is a knave.
 Assume Grace is a knave.  No contradiction is found in their false claim that Harper is a knight and Grace is a knight.
 Aurora cannot be a knight, because this would contradict the claim of Harper that Ethan is a knave if and only if Aurora is a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that If Mason is a knight then Mason is a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that Harper is a knave if and only if Ava is a knave.
 Ava cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Ava is a knight.
 Ava cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Ava is a knight.
 We have exhausted all possibilities for Ava, so let us go back and reconsider Mason.
 Mason cannot be a knave, because this would contradict the false claim of Aurora that If Mason is a knight then Mason is a knave.
 We have exhausted all possibilities for Mason, Aurora, and Grace, so let us go back and reconsider Ethan.
 Assume Ethan is a knave.  No contradiction is found in their false claim that If Harper is a knight then Grace is a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that Harper is a knight and Grace is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that If Mason is a knight then Mason is a knave.
 Mason cannot be a knight, because this would contradict the claim of Aurora that If Mason is a knight then Mason is a knave.
 Assume Mason is a knave.  No contradiction is found in their false claim that Harper is a knave if and only if Ava is a knave.
 Ava cannot be a knight, because this would contradict the false claim of Mason that Harper is a knave if and only if Ava is a knave.
 Assume Ava is a knave.  No contradiction is found in their false claim that Grace is a knight if and only if Ava is a knight.
 Jackson cannot be a knight, because this would contradict the claim of their own that Mason is a knight or Harper is a knave.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Mason is a knight or Harper is a knave.
 Therefore, (1) Harper is a knight
 (2) Ethan is a knave
 (3) Grace is a knight
 (4) Aurora is a knight
 (5) Ava is a knave
 (6) Mason is a knave
 (7) Jackson 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 7 inhabitants: Harper, Ethan, Grace, Aurora, Ava, Mason, and Jackson. Harper remarked, "Ethan is a knave if and only if Aurora is a knight". Ethan said, "If Harper is a knight then Grace is a knave." In a statement by Grace: "Harper is a knight and Grace is a knight". "If Mason is a knight then Mason is a knave" - Aurora. According to Ava, "Grace is a knight if and only if Ava is a knight". Mason said that Harper is a knave if and only if Ava is a knave. Jackson remarked, "Mason is a knight or Harper is 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 Harper is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Aurora is a knight.
Assume Ethan is a knight. No contradiction is found in their claim that If Harper is a knight then Grace is a knave.
Grace cannot be a knight, because this would contradict the claim of Ethan that If Harper is a knight then Grace is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Harper is a knight and Grace is a knight.
Aurora cannot be a knight, because this would contradict the claim of Harper that Ethan is a knave if and only if Aurora is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that If Mason is a knight then Mason is a knave.
Assume Mason is a knight. No contradiction is found in their claim that Harper is a knave if and only if Ava is a knave.
Ava cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Ava is a knight.
Ava cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Ava is a knight.
We have exhausted all possibilities for Ava, so let us go back and reconsider Mason.
Mason cannot be a knave, because this would contradict the false claim of Aurora that If Mason is a knight then Mason is a knave.
We have exhausted all possibilities for Mason, Aurora, and Grace, so let us go back and reconsider Ethan.
Assume Ethan is a knave. No contradiction is found in their false claim that If Harper is a knight then Grace is a knave.
Assume Grace is a knight. No contradiction is found in their claim that Harper is a knight and Grace is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that If Mason is a knight then Mason is a knave.
Mason cannot be a knight, because this would contradict the claim of Aurora that If Mason is a knight then Mason is a knave.
Assume Mason is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Ava is a knave.
Ava cannot be a knight, because this would contradict the false claim of Mason that Harper is a knave if and only if Ava is a knave.
Assume Ava is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Ava is a knight.
Jackson cannot be a knight, because this would contradict the claim of their own that Mason is a knight or Harper is a knave.
Assume Jackson is a knave. No contradiction is found in their false claim that Mason is a knight or Harper is a knave.
Therefore, (1) Harper is a knight
(2) Ethan is a knave
(3) Grace is a knight
(4) Aurora is a knight
(5) Ava is a knave
(6) Mason is a knave
(7) Jackson is a knave </think>
<answer> (1) Harper is a knight
(2) Ethan is a knave
(3) Grace is a knight
(4) Aurora is a knight
(5) Ava is a knave
(6) Mason is a knave
(7) Jackson is a knave </answer>
Harper Ethan Grace Aurora Ava Mason Jackson
(1) Harper is a knight
(2) Ethan is a knave
(3) Grace is a knight
(4) Aurora is a knight
(5) Ava is a knave
(6) Mason is a knave
(7) Jackson is a knave
(('<=>', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('lying', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('lying', 0), ('lying', 4)), ('or', ('telling-truth', 5), ('lying', 0)))
rule