
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  $\mathbb{N}$  denote the set of positive integers. Find all functions  $f \colon \mathbb{N} \to \mathbb{Z}$  such that \[\left\lfloor \frac{f(mn)}{n} \right\rfloor=f(m)\] for all positive integers  $m,n$ .

*Merlijn Staps*

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