
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
Given real numbers \( a_1, a_2, \ldots, a_{2013} \) (which may include repetitions) with an arithmetic mean of \( m \), we define a set \(\{i, j, k\}\) to be an optimal group if it satisfies
\[ a_i + a_j + a_k \geq 3m \quad (1 \leq i < j < k \leq 2013). \]

Determine the minimum possible number of optimal groups.

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