<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Given a circle $C: x^2 + y^2 + mx - 4 = 0$, there exist two points on the circle that are symmetric with respect to the line $x - y + 3 = 0$. Find the value of the real number $m$. Express your answer as a single real number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
6
Given a circle $C: x^2 + y^2 + mx - 4 = 0$, there exist two points on the circle that are symmetric with respect to the line $x - y + 3 = 0$. Find the value of the real number $m$. Express your answer as a single real number.
test