
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
Determine the least possible value of \( f(1998) \), where \( f \) is a function from the set \(\mathbb{N}\) of positive integers into itself such that for all \( m, n \in \mathbb{N} \),
\[ f\left(n^{2} f(m)\right) = m [f(n)]^{2}. \]

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