
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
Consider the set  $M=\{1,2,...,n\},n\in\mathbb N$ . Find the smallest positive integer  $k$  with the following property: In every  $k$ -element subset  $S$  of  $M$  there exist two elements, one of which divides the other one.


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