
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 a sequence \( A = a_1, a_2, \cdots, a_{2005} \) with \( a_i \in \mathbf{N}^{+} \), let \( m(A) \) be the number of triplets \(\left(a_i, a_j, a_k\right)\) that satisfy \(a_j = a_i + 1\) and \(a_k = a_j + 1\) for \(1 \leq i < j < k \leq 2005\). Determine the maximum value of \( m(A) \) for all possible sequences \( A \).

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