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 4 inhabitants: Ethan, Aurora, Lily, and Victoria. "Ethan is a knight and Victoria is a knight," Ethan declared. Aurora stated, "Victoria is a knave or Ethan is a knight". In Lily's words: "Aurora is not a knave". Victoria said, "Aurora is a knight or Lily is a knight." 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 Ethan is a knight.  No contradiction is found in their claim that Ethan is a knight and Victoria is a knight.
 Assume Victoria is a knight.  No contradiction is found in their claim that Aurora is a knight or Lily is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Victoria is a knave or Ethan is a knight.
 Assume Lily is a knight.  No contradiction is found in their claim that Aurora is not a knave.
 Therefore, (1) Ethan is a knight
 (2) Aurora is a knight
 (3) Lily is a knight
 (4) Victoria 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 4 inhabitants: Ethan, Aurora, Lily, and Victoria. "Ethan is a knight and Victoria is a knight," Ethan declared. Aurora stated, "Victoria is a knave or Ethan is a knight". In Lily's words: "Aurora is not a knave". Victoria said, "Aurora is a knight or Lily is a knight." 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 Ethan is a knight. No contradiction is found in their claim that Ethan is a knight and Victoria is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that Aurora is a knight or Lily is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Victoria is a knave or Ethan is a knight.
Assume Lily is a knight. No contradiction is found in their claim that Aurora is not a knave.
Therefore, (1) Ethan is a knight
(2) Aurora is a knight
(3) Lily is a knight
(4) Victoria is a knight </think>
<answer> (1) Ethan is a knight
(2) Aurora is a knight
(3) Lily is a knight
(4) Victoria is a knight </answer>
Ethan Aurora Lily Victoria
(1) Ethan is a knight
(2) Aurora is a knight
(3) Lily is a knight
(4) Victoria is a knight
(('and', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('lying', 3), ('telling-truth', 0)), ('not', ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 2)))
rule