
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
For integers $n \geqslant 4$, find the smallest integer $f(n)$ such that for any positive integer $m$, any $f(n)$-element subset of the set $\{m, m+1, \cdots, m+n-1\}$ contains at least 3 pairwise coprime elements.

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