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: Jackson, Aurora, and Lucas. As Jackson put it, "If Aurora is a knave then Lucas is a knight". As Aurora put it, "Lucas is a knave if and only if Aurora is a knight". In Lucas's words: "Lucas is a knight or 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 Jackson is a knight.  No contradiction is found in their claim that If Aurora is a knave then Lucas is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Lucas is a knave if and only if Aurora is a knight.
 Lucas cannot be a knight, because this would contradict the claim of Aurora that Lucas is a knave if and only if Aurora is a knight.
 Assume Lucas is a knave.  No contradiction is found in their false claim that Lucas is a knight or Aurora is a knave.
 Therefore, (1) Jackson is a knight
 (2) Aurora 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: Jackson, Aurora, and Lucas. As Jackson put it, "If Aurora is a knave then Lucas is a knight". As Aurora put it, "Lucas is a knave if and only if Aurora is a knight". In Lucas's words: "Lucas is a knight or 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 Jackson is a knight. No contradiction is found in their claim that If Aurora is a knave then Lucas is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Aurora is a knight.
Lucas cannot be a knight, because this would contradict the claim of Aurora that Lucas is a knave if and only if Aurora is a knight.
Assume Lucas is a knave. No contradiction is found in their false claim that Lucas is a knight or Aurora is a knave.
Therefore, (1) Jackson is a knight
(2) Aurora is a knight
(3) Lucas is a knave </think>
<answer> (1) Jackson is a knight
(2) Aurora is a knight
(3) Lucas is a knave </answer>
Jackson Aurora Lucas
(1) Jackson is a knight
(2) Aurora is a knight
(3) Lucas is a knave
(('->', ('lying', 1), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 1)))
rule