
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
A positive integer  $n\geq 4$  is called *interesting* if there exists a complex number  $z$  such that  $|z|=1$  and \[1+z+z^2+z^{n-1}+z^n=0.\] Find how many interesting numbers are smaller than  $2022.$ 

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