
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
Find all numbers  $n \in \mathbb{N}^*$  for which there exists a finite set of natural numbers  $A=(a_1, a_2,...a_n)$  so that for any  $k$   $(1\leq k \leq n)$  the number  $a_k$  is the number of all multiples of  $k$  in set  $A$ .

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