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 7 inhabitants: Jackson, Lucas, Jacob, Matthew, Evelyn, Elizabeth, and Alexander. Jackson was heard saying, "If Evelyn is a knave then Jackson is a knight". Lucas expressed that Alexander is a knave and Elizabeth is a knight. Jacob commented, "Alexander is a knight". In Matthew's words: "Evelyn is a knight and Alexander is a knight". "Matthew is not a knight," Evelyn claimed. According to Elizabeth, "Jacob is a knave". Alexander remarked, "Matthew is a knight and Evelyn 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 Evelyn is a knave then Jackson is a knight.
 Assume Evelyn is a knight.  No contradiction is found in their claim that Matthew is not a knight.
 Matthew cannot be a knight, because this would contradict the claim of Evelyn that Matthew is not a knight.
 Assume Matthew is a knave.  No contradiction is found in their false claim that Evelyn is a knight and Alexander is a knight.
 Alexander cannot be a knight, because this would contradict the false claim of Matthew that Evelyn is a knight and Alexander is a knight.
 Assume Alexander is a knave.  No contradiction is found in their false claim that Matthew is a knight and Evelyn is a knave.
 Assume Lucas is a knight.  No contradiction is found in their claim that Alexander is a knave and Elizabeth is a knight.
 Assume Elizabeth is a knight.  No contradiction is found in their claim that Jacob is a knave.
 Jacob cannot be a knight, because this would contradict the claim of their own that Alexander is a knight.
 Assume Jacob is a knave.  No contradiction is found in their false claim that Alexander is a knight.
 Therefore, (1) Jackson is a knight
 (2) Lucas is a knight
 (3) Jacob is a knave
 (4) Matthew is a knave
 (5) Evelyn is a knight
 (6) Elizabeth is a knight
 (7) Alexander 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 7 inhabitants: Jackson, Lucas, Jacob, Matthew, Evelyn, Elizabeth, and Alexander. Jackson was heard saying, "If Evelyn is a knave then Jackson is a knight". Lucas expressed that Alexander is a knave and Elizabeth is a knight. Jacob commented, "Alexander is a knight". In Matthew's words: "Evelyn is a knight and Alexander is a knight". "Matthew is not a knight," Evelyn claimed. According to Elizabeth, "Jacob is a knave". Alexander remarked, "Matthew is a knight and Evelyn 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 Evelyn is a knave then Jackson is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is not a knight.
Matthew cannot be a knight, because this would contradict the claim of Evelyn that Matthew is not a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that Evelyn is a knight and Alexander is a knight.
Alexander cannot be a knight, because this would contradict the false claim of Matthew that Evelyn is a knight and Alexander is a knight.
Assume Alexander is a knave. No contradiction is found in their false claim that Matthew is a knight and Evelyn is a knave.
Assume Lucas is a knight. No contradiction is found in their claim that Alexander is a knave and Elizabeth is a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that Jacob is a knave.
Jacob cannot be a knight, because this would contradict the claim of their own that Alexander is a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that Alexander is a knight.
Therefore, (1) Jackson is a knight
(2) Lucas is a knight
(3) Jacob is a knave
(4) Matthew is a knave
(5) Evelyn is a knight
(6) Elizabeth is a knight
(7) Alexander is a knave </think>
<answer> (1) Jackson is a knight
(2) Lucas is a knight
(3) Jacob is a knave
(4) Matthew is a knave
(5) Evelyn is a knight
(6) Elizabeth is a knight
(7) Alexander is a knave </answer>
Jackson Lucas Jacob Matthew Evelyn Elizabeth Alexander
(1) Jackson is a knight
(2) Lucas is a knight
(3) Jacob is a knave
(4) Matthew is a knave
(5) Evelyn is a knight
(6) Elizabeth is a knight
(7) Alexander is a knave
(('->', ('lying', 4), ('telling-truth', 0)), ('and', ('lying', 6), ('telling-truth', 5)), ('telling-truth', 6), ('and', ('telling-truth', 4), ('telling-truth', 6)), ('not', ('telling-truth', 3)), ('lying', 2), ('and', ('telling-truth', 3), ('lying', 4)))
rule