
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 integer  $n\ge 4$ , find the minimal integer  $f(n)$ , such that for any positive integer  $m$ , in any subset with  $f(n)$  elements of the set  ${m, m+1, \ldots, m+n+1}$  there are at least  $3$  relatively prime elements.

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