
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 an integer  $n \ge 3$  we consider a circle with  $n$  points on it.
We place a positive integer at each point, where the numbers are not necessary need to be different. Such placement of numbers is called *stable* as three numbers next to always have product  $n$  each other. 
For how many values of  $n$  with  $3 \le n \le 2020$  is it possible to place numbers in a stable way?


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