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: Henry, Jack, Amelia, and Evelyn. Henry was heard saying, "Jack is a knave if and only if Henry is a knight". Jack commented, "Henry is not a knight". Amelia expressed that Evelyn is a knave. In a statement by Evelyn: "Jack is a knight and Henry 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 Henry is a knight.  No contradiction is found in their claim that Jack is a knave if and only if Henry is a knight.
 Jack cannot be a knight, because this would contradict the claim of Henry that Jack is a knave if and only if Henry is a knight.
 Assume Jack is a knave.  No contradiction is found in their false claim that Henry is not a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that Evelyn is a knave.
 Evelyn cannot be a knight, because this would contradict the claim of Amelia that Evelyn is a knave.
 Assume Evelyn is a knave.  No contradiction is found in their false claim that Jack is a knight and Henry is a knight.
 Therefore, (1) Henry is a knight
 (2) Jack is a knave
 (3) Amelia is a knight
 (4) Evelyn 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 4 inhabitants: Henry, Jack, Amelia, and Evelyn. Henry was heard saying, "Jack is a knave if and only if Henry is a knight". Jack commented, "Henry is not a knight". Amelia expressed that Evelyn is a knave. In a statement by Evelyn: "Jack is a knight and Henry 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 Henry is a knight. No contradiction is found in their claim that Jack is a knave if and only if Henry is a knight.
Jack cannot be a knight, because this would contradict the claim of Henry that Jack is a knave if and only if Henry is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Henry is not a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Evelyn is a knave.
Evelyn cannot be a knight, because this would contradict the claim of Amelia that Evelyn is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Jack is a knight and Henry is a knight.
Therefore, (1) Henry is a knight
(2) Jack is a knave
(3) Amelia is a knight
(4) Evelyn is a knave </think>
<answer> (1) Henry is a knight
(2) Jack is a knave
(3) Amelia is a knight
(4) Evelyn is a knave </answer>
Henry Jack Amelia Evelyn
(1) Henry is a knight
(2) Jack is a knave
(3) Amelia is a knight
(4) Evelyn is a knave
(('<=>', ('lying', 1), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('lying', 3), ('and', ('telling-truth', 1), ('telling-truth', 0)))
rule