
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 \( A = \left(a_1, a_2, \ldots, a_{2001}\right) \) be a sequence of positive integers. Let \( m \) be the number of 3-element subsequences \( (a_i, a_j, a_k) \) with \( 1 \leq i < j < k \leq 2001 \) such that \( a_j = a_i + 1 \) and \( a_k = a_j + 1 \). Considering all such sequences \( A \), find the greatest value of \( m \).

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