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: Aurora, Grace, Harper, Amelia, Oliver, Elizabeth, and Emily. As Aurora put it, "Oliver is a knave or Amelia is a knight". Grace was heard saying, "Aurora is not a knave". In a statement by Harper: "Emily is a knave or Grace is a knight". Amelia remarked, "Aurora is a knave and Harper is a knight". Oliver said, "Amelia is a knight and Harper is a knight." "Emily is a knight," Elizabeth mentioned. Emily told you that Aurora 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 Aurora is a knight.  No contradiction is found in their claim that Oliver is a knave or Amelia is a knight.
 Assume Oliver is a knight.  No contradiction is found in their claim that Amelia is a knight and Harper is a knight.
 Amelia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Harper is a knight.
 Amelia cannot be a knave, because this would contradict the claim of Aurora that Oliver is a knave or Amelia is a knight.
 We have exhausted all possibilities for Amelia, so let us go back and reconsider Oliver.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Amelia is a knight and Harper is a knight.
 Amelia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Harper is a knight.
 Assume Amelia is a knave.  No contradiction is found in their false claim that Aurora is a knave and Harper is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Emily is a knave or Grace is a knight.
 Emily cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.
 Assume Emily is a knave.  No contradiction is found in their false claim that Aurora is a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that Aurora is not a knave.
 Elizabeth cannot be a knight, because this would contradict the claim of their own that Emily is a knight.
 Assume Elizabeth is a knave.  No contradiction is found in their false claim that Emily is a knight.
 Therefore, (1) Aurora is a knight
 (2) Grace is a knight
 (3) Harper is a knight
 (4) Amelia is a knave
 (5) Oliver is a knave
 (6) Elizabeth is a knave
 (7) Emily 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: Aurora, Grace, Harper, Amelia, Oliver, Elizabeth, and Emily. As Aurora put it, "Oliver is a knave or Amelia is a knight". Grace was heard saying, "Aurora is not a knave". In a statement by Harper: "Emily is a knave or Grace is a knight". Amelia remarked, "Aurora is a knave and Harper is a knight". Oliver said, "Amelia is a knight and Harper is a knight." "Emily is a knight," Elizabeth mentioned. Emily told you that Aurora 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 Aurora is a knight. No contradiction is found in their claim that Oliver is a knave or Amelia is a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Amelia is a knight and Harper is a knight.
Amelia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Harper is a knight.
Amelia cannot be a knave, because this would contradict the claim of Aurora that Oliver is a knave or Amelia is a knight.
We have exhausted all possibilities for Amelia, so let us go back and reconsider Oliver.
Assume Oliver is a knave. No contradiction is found in their false claim that Amelia is a knight and Harper is a knight.
Amelia cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Harper is a knight.
Assume Amelia is a knave. No contradiction is found in their false claim that Aurora is a knave and Harper is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Emily is a knave or Grace is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.
Assume Emily is a knave. No contradiction is found in their false claim that Aurora is a knave.
Assume Grace is a knight. No contradiction is found in their claim that Aurora is not a knave.
Elizabeth cannot be a knight, because this would contradict the claim of their own that Emily is a knight.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Emily is a knight.
Therefore, (1) Aurora is a knight
(2) Grace is a knight
(3) Harper is a knight
(4) Amelia is a knave
(5) Oliver is a knave
(6) Elizabeth is a knave
(7) Emily is a knave </think>
<answer> (1) Aurora is a knight
(2) Grace is a knight
(3) Harper is a knight
(4) Amelia is a knave
(5) Oliver is a knave
(6) Elizabeth is a knave
(7) Emily is a knave </answer>
Aurora Grace Harper Amelia Oliver Elizabeth Emily
(1) Aurora is a knight
(2) Grace is a knight
(3) Harper is a knight
(4) Amelia is a knave
(5) Oliver is a knave
(6) Elizabeth is a knave
(7) Emily is a knave
(('or', ('lying', 4), ('telling-truth', 3)), ('not', ('lying', 0)), ('or', ('lying', 6), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 6), ('lying', 0))
rule