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: Lily, Oliver, Grace, and Mason. "Oliver is a knave," Lily declared. Oliver was heard saying, "Grace is not a knight". In Grace's words: "Oliver is a knave or Mason is a knave". Mason noted, "If Mason is a knight then Grace 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 Lily is a knight.  No contradiction is found in their claim that Oliver is a knave.
 Oliver cannot be a knight, because this would contradict the claim of Lily that Oliver is a knave.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Grace is not a knight.
 Assume Grace is a knight.  No contradiction is found in their claim that Oliver is a knave or Mason is a knave.
 Mason cannot be a knight, because this would contradict the claim of their own that If Mason is a knight then Grace is a knave.
 Mason cannot be a knave, because this would contradict the false claim of their own that If Mason is a knight then Grace is a knave.
 We have exhausted all possibilities for Mason, so let us go back and reconsider Grace.
 Grace cannot be a knave, because this would contradict the false claim of Oliver that Grace is not a knight.
 We have exhausted all possibilities for Grace and Oliver, so let us go back and reconsider Lily.
 Assume Lily is a knave.  No contradiction is found in their false claim that Oliver is a knave.
 Assume Oliver is a knight.  No contradiction is found in their claim that Grace is not a knight.
 Grace cannot be a knight, because this would contradict the claim of Oliver that Grace is not a knight.
 Assume Grace is a knave.  No contradiction is found in their false claim that Oliver is a knave or Mason is a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that If Mason is a knight then Grace is a knave.
 Therefore, (1) Lily is a knave
 (2) Oliver is a knight
 (3) Grace is a knave
 (4) Mason 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: Lily, Oliver, Grace, and Mason. "Oliver is a knave," Lily declared. Oliver was heard saying, "Grace is not a knight". In Grace's words: "Oliver is a knave or Mason is a knave". Mason noted, "If Mason is a knight then Grace 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 Lily is a knight. No contradiction is found in their claim that Oliver is a knave.
Oliver cannot be a knight, because this would contradict the claim of Lily that Oliver is a knave.
Assume Oliver is a knave. No contradiction is found in their false claim that Grace is not a knight.
Assume Grace is a knight. No contradiction is found in their claim that Oliver is a knave or Mason is a knave.
Mason cannot be a knight, because this would contradict the claim of their own that If Mason is a knight then Grace is a knave.
Mason cannot be a knave, because this would contradict the false claim of their own that If Mason is a knight then Grace is a knave.
We have exhausted all possibilities for Mason, so let us go back and reconsider Grace.
Grace cannot be a knave, because this would contradict the false claim of Oliver that Grace is not a knight.
We have exhausted all possibilities for Grace and Oliver, so let us go back and reconsider Lily.
Assume Lily is a knave. No contradiction is found in their false claim that Oliver is a knave.
Assume Oliver is a knight. No contradiction is found in their claim that Grace is not a knight.
Grace cannot be a knight, because this would contradict the claim of Oliver that Grace is not a knight.
Assume Grace is a knave. No contradiction is found in their false claim that Oliver is a knave or Mason is a knave.
Assume Mason is a knight. No contradiction is found in their claim that If Mason is a knight then Grace is a knave.
Therefore, (1) Lily is a knave
(2) Oliver is a knight
(3) Grace is a knave
(4) Mason is a knight </think>
<answer> (1) Lily is a knave
(2) Oliver is a knight
(3) Grace is a knave
(4) Mason is a knight </answer>
Lily Oliver Grace Mason
(1) Lily is a knave
(2) Oliver is a knight
(3) Grace is a knave
(4) Mason is a knight
(('lying', 1), ('not', ('telling-truth', 2)), ('or', ('lying', 1), ('lying', 3)), ('->', ('telling-truth', 3), ('lying', 2)))
rule