
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 \( f: \mathbf{N}^{*} \rightarrow \mathbf{N} \), where for any \( m, n \in \mathbf{N}^{*} \), it holds that \( f(m+n) \geq f(m) + f(n) \). Given that \( f(2) = 0 \), \( f(3) > 0 \), and \( f(9999) = 3333 \), find \( f(1997) \).

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