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 5 inhabitants: Amelia, Zoey, Avery, Lily, and Daniel. In Amelia's words: "If Daniel is a knave then Lily is a knight". Zoey asserted: "Avery is a knave and Avery is a knight". In Avery's words: "Lily is not a knight". "Daniel is a knight or Avery is a knight," Lily declared. "Daniel is a knight and Amelia is a knight," Daniel declared. 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 Amelia is a knight.  No contradiction is found in their claim that If Daniel is a knave then Lily is a knight.
 Assume Daniel is a knight.  No contradiction is found in their claim that Daniel is a knight and Amelia is a knight.
 Assume Lily is a knight.  No contradiction is found in their claim that Daniel is a knight or Avery is a knight.
 Avery cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.
 Assume Avery is a knave.  No contradiction is found in their false claim that Lily is not a knight.
 Zoey cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Avery is a knight.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Avery is a knave and Avery is a knight.
 Therefore, (1) Amelia is a knight
 (2) Zoey is a knave
 (3) Avery is a knave
 (4) Lily is a knight
 (5) Daniel 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 5 inhabitants: Amelia, Zoey, Avery, Lily, and Daniel. In Amelia's words: "If Daniel is a knave then Lily is a knight". Zoey asserted: "Avery is a knave and Avery is a knight". In Avery's words: "Lily is not a knight". "Daniel is a knight or Avery is a knight," Lily declared. "Daniel is a knight and Amelia is a knight," Daniel declared. 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 Amelia is a knight. No contradiction is found in their claim that If Daniel is a knave then Lily is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight and Amelia is a knight.
Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knight or Avery is a knight.
Avery cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.
Assume Avery is a knave. No contradiction is found in their false claim that Lily is not a knight.
Zoey cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Avery is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Avery is a knave and Avery is a knight.
Therefore, (1) Amelia is a knight
(2) Zoey is a knave
(3) Avery is a knave
(4) Lily is a knight
(5) Daniel is a knight </think>
<answer> (1) Amelia is a knight
(2) Zoey is a knave
(3) Avery is a knave
(4) Lily is a knight
(5) Daniel is a knight </answer>
Amelia Zoey Avery Lily Daniel
(1) Amelia is a knight
(2) Zoey is a knave
(3) Avery is a knave
(4) Lily is a knight
(5) Daniel is a knight
(('->', ('lying', 4), ('telling-truth', 3)), ('and', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('telling-truth', 4), ('telling-truth', 0)))
rule