
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 the function \( f: \mathbf{Z}_{+} \rightarrow \mathbf{Z}_{+} \) satisfy: for any \( n \in \mathbf{Z}_{+} \),
\[ n^{3}-n^{2} \leqslant f(n) f^{2}(f(n)) \leqslant n^{3}+n^{2} \text{.} \]

Find the function \( f \).

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