
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 \(\mathbb{N}^{*}\) be the set of strictly positive integers. Determine all functions \(f\) from \(\mathbb{N}^{*}\) to \(\mathbb{N}^{*}\) such that, for all \(m, n \in \(\mathbb{N}^{*}\), we have

$$
n+f(m) \mid f(n)+n f(m)
$$

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