
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 \( f \) be a function defined on the set of positive integers, such that for all \( m, n \in \mathbf{N}^{+} \), \( f(m \cdot n) = f(m) + f(n) \), and \( f(n+1) \geqslant f(n) \). Find \( f(n) \).

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