
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  $n \geq 2$  be an integer. Let  $S$  be a subset of  $\{1,2,\dots,n\}$  such that  $S$  neither contains two elements one of which divides the other, nor contains two elements which are coprime. What is the maximal possible number of elements of such a set  $S$ ?

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