<|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
 Let \( a_{1}, a_{2}, \ldots, a_{9} \) be nine real numbers, not necessarily distinct, with average \( m \). Let \( A \) denote the number of triples \( 1 \leq i<j<k \leq 9 \) for which \( a_{i}+a_{j}+a_{k} \geq 3m \). What is the minimum possible value of \( A \)? 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
28
Let \( a_{1}, a_{2}, \ldots, a_{9} \) be nine real numbers, not necessarily distinct, with average \( m \). Let \( A \) denote the number of triples \( 1 \leq i<j<k \leq 9 \) for which \( a_{i}+a_{j}+a_{k} \geq 3m \). What is the minimum possible value of \( A \)?
test