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: Emma, Sebastian, Owen, and Avery. "Avery is a knave or Emma is a knight," Emma claimed. Sebastian remarked, "Avery is not a knight". Owen noted, "Avery is a knight or Avery is a knave". Avery asserted: "Emma is a knight and Owen 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 Emma is a knight.  No contradiction is found in their claim that Avery is a knave or Emma is a knight.
 Assume Avery is a knight.  No contradiction is found in their claim that Emma is a knight and Owen is a knight.
 Assume Owen is a knight.  No contradiction is found in their claim that Avery is a knight or Avery is a knave.
 Sebastian cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Avery is not a knight.
 Therefore, (1) Emma is a knight
 (2) Sebastian is a knave
 (3) Owen is a knight
 (4) Avery 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: Emma, Sebastian, Owen, and Avery. "Avery is a knave or Emma is a knight," Emma claimed. Sebastian remarked, "Avery is not a knight". Owen noted, "Avery is a knight or Avery is a knave". Avery asserted: "Emma is a knight and Owen 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 Emma is a knight. No contradiction is found in their claim that Avery is a knave or Emma is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Emma is a knight and Owen is a knight.
Assume Owen is a knight. No contradiction is found in their claim that Avery is a knight or Avery is a knave.
Sebastian cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.
Assume Sebastian is a knave. No contradiction is found in their false claim that Avery is not a knight.
Therefore, (1) Emma is a knight
(2) Sebastian is a knave
(3) Owen is a knight
(4) Avery is a knight </think>
<answer> (1) Emma is a knight
(2) Sebastian is a knave
(3) Owen is a knight
(4) Avery is a knight </answer>
Emma Sebastian Owen Avery
(1) Emma is a knight
(2) Sebastian is a knave
(3) Owen is a knight
(4) Avery is a knight
(('or', ('lying', 3), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 0), ('telling-truth', 2)))
rule