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 3 inhabitants: Aurora, Noah, and Lucas. Aurora told you that If Lucas is a knave then Noah is a knight. According to Noah, "Lucas is a knave". Lucas expressed that Noah is a knight and Noah 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 If Lucas is a knave then Noah is a knight.
 Lucas cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Noah is a knave.
 Assume Lucas is a knave.  No contradiction is found in their false claim that Noah is a knight and Noah is a knave.
 Assume Noah is a knight.  No contradiction is found in their claim that Lucas is a knave.
 Therefore, (1) Aurora is a knight
 (2) Noah is a knight
 (3) Lucas 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 3 inhabitants: Aurora, Noah, and Lucas. Aurora told you that If Lucas is a knave then Noah is a knight. According to Noah, "Lucas is a knave". Lucas expressed that Noah is a knight and Noah 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 If Lucas is a knave then Noah is a knight.
Lucas cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Noah is a knave.
Assume Lucas is a knave. No contradiction is found in their false claim that Noah is a knight and Noah is a knave.
Assume Noah is a knight. No contradiction is found in their claim that Lucas is a knave.
Therefore, (1) Aurora is a knight
(2) Noah is a knight
(3) Lucas is a knave </think>
<answer> (1) Aurora is a knight
(2) Noah is a knight
(3) Lucas is a knave </answer>
Aurora Noah Lucas
(1) Aurora is a knight
(2) Noah is a knight
(3) Lucas is a knave
(('->', ('lying', 2), ('telling-truth', 1)), ('lying', 2), ('and', ('telling-truth', 1), ('lying', 1)))
rule