
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
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 \( A \)?

Present the answer in LaTex format: \boxed{Your answer}
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