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 5 inhabitants: Riley, Aria, Lily, Mason, and Michael. As Riley put it, "Lily is a knight or Mason is a knave". Aria expressed that Lily is a knave if and only if Mason is a knight. "Lily is a knight or Aria is a knight," Lily claimed. Mason noted, "Lily is a knave or Michael is a knight". Michael noted, "Lily is a knave if and only if 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 Riley is a knight.  No contradiction is found in their claim that Lily is a knight or Mason is a knave.
 Assume Lily is a knight.  No contradiction is found in their claim that Lily is a knight or Aria is a knight.
 Assume Aria is a knight.  No contradiction is found in their claim that Lily is a knave if and only if Mason is a knight.
 Mason cannot be a knight, because this would contradict the claim of Aria that Lily is a knave if and only if Mason is a knight.
 Assume Mason is a knave.  No contradiction is found in their false claim that Lily is a knave or Michael is a knight.
 Michael cannot be a knight, because this would contradict the false claim of Mason that Lily is a knave or Michael is a knight.
 Assume Michael is a knave.  No contradiction is found in their false claim that Lily is a knave if and only if Lily is a knight.
 Therefore, (1) Riley is a knight
 (2) Aria is a knight
 (3) Lily is a knight
 (4) Mason is a knave
 (5) Michael 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 5 inhabitants: Riley, Aria, Lily, Mason, and Michael. As Riley put it, "Lily is a knight or Mason is a knave". Aria expressed that Lily is a knave if and only if Mason is a knight. "Lily is a knight or Aria is a knight," Lily claimed. Mason noted, "Lily is a knave or Michael is a knight". Michael noted, "Lily is a knave if and only if 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 Riley is a knight. No contradiction is found in their claim that Lily is a knight or Mason is a knave.
Assume Lily is a knight. No contradiction is found in their claim that Lily is a knight or Aria is a knight.
Assume Aria is a knight. No contradiction is found in their claim that Lily is a knave if and only if Mason is a knight.
Mason cannot be a knight, because this would contradict the claim of Aria that Lily is a knave if and only if Mason is a knight.
Assume Mason is a knave. No contradiction is found in their false claim that Lily is a knave or Michael is a knight.
Michael cannot be a knight, because this would contradict the false claim of Mason that Lily is a knave or Michael is a knight.
Assume Michael is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Lily is a knight.
Therefore, (1) Riley is a knight
(2) Aria is a knight
(3) Lily is a knight
(4) Mason is a knave
(5) Michael is a knave </think>
<answer> (1) Riley is a knight
(2) Aria is a knight
(3) Lily is a knight
(4) Mason is a knave
(5) Michael is a knave </answer>
Riley Aria Lily Mason Michael
(1) Riley is a knight
(2) Aria is a knight
(3) Lily is a knight
(4) Mason is a knave
(5) Michael is a knave
(('or', ('telling-truth', 2), ('lying', 3)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 2)))
rule