<|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
 How many graphs are there on 10 vertices labeled \(1,2, \ldots, 10\) such that there are exactly 23 edges and no triangles? 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
42840
How many graphs are there on 10 vertices labeled \(1,2, \ldots, 10\) such that there are exactly 23 edges and no triangles?
test