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: Joseph, Avery, Amelia, Elizabeth, Emma, and Liam. Joseph was heard saying, "Amelia is a knight or Avery is a knight". Avery expressed that Elizabeth is a knave. In a statement by Amelia: "Joseph is a knight if and only if Avery is a knight". Elizabeth stated, "Emma is a knave and Joseph is a knave". "Avery is not a knight," Emma declared. Liam expressed that Avery is a knight if and only if Emma 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 Joseph is a knight.  No contradiction is found in their claim that Amelia is a knight or Avery is a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that Joseph is a knight if and only if Avery is a knight.
 Assume Avery is a knight.  No contradiction is found in their claim that Elizabeth is a knave.
 Elizabeth cannot be a knight, because this would contradict the claim of Avery that Elizabeth is a knave.
 Assume Elizabeth is a knave.  No contradiction is found in their false claim that Emma is a knave and Joseph is a knave.
 Emma cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.
 Assume Emma is a knave.  No contradiction is found in their false claim that Avery is not a knight.
 Assume Liam is a knight.  No contradiction is found in their claim that Avery is a knight if and only if Emma is a knave.
 Therefore, (1) Joseph is a knight
 (2) Avery is a knight
 (3) Amelia is a knight
 (4) Elizabeth is a knave
 (5) Emma is a knave
 (6) Liam is a knight
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: Joseph, Avery, Amelia, Elizabeth, Emma, and Liam. Joseph was heard saying, "Amelia is a knight or Avery is a knight". Avery expressed that Elizabeth is a knave. In a statement by Amelia: "Joseph is a knight if and only if Avery is a knight". Elizabeth stated, "Emma is a knave and Joseph is a knave". "Avery is not a knight," Emma declared. Liam expressed that Avery is a knight if and only if Emma 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 Joseph is a knight. No contradiction is found in their claim that Amelia is a knight or Avery is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Avery is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Elizabeth is a knave.
Elizabeth cannot be a knight, because this would contradict the claim of Avery that Elizabeth is a knave.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Emma is a knave and Joseph is a knave.
Emma cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.
Assume Emma is a knave. No contradiction is found in their false claim that Avery is not a knight.
Assume Liam is a knight. No contradiction is found in their claim that Avery is a knight if and only if Emma is a knave.
Therefore, (1) Joseph is a knight
(2) Avery is a knight
(3) Amelia is a knight
(4) Elizabeth is a knave
(5) Emma is a knave
(6) Liam is a knight </think>
<answer> (1) Joseph is a knight
(2) Avery is a knight
(3) Amelia is a knight
(4) Elizabeth is a knave
(5) Emma is a knave
(6) Liam is a knight </answer>
Joseph Avery Amelia Elizabeth Emma Liam
(1) Joseph is a knight
(2) Avery is a knight
(3) Amelia is a knight
(4) Elizabeth is a knave
(5) Emma is a knave
(6) Liam is a knight
(('or', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 3), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('lying', 4), ('lying', 0)), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 4)))
rule