
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 each integer  $n\geq 3$ , find the least natural number  $f(n)$  having the property  $\star$  For every  $A \subset \{1, 2, \ldots, n\}$  with  $f(n)$  elements, there exist elements  $x, y, z \in A$  that are pairwise coprime.

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