
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
Nicky has a circle. To make his circle look more interesting, he draws a regular 15-gon, 21-gon, and 35-gon such that all vertices of all three polygons lie on the circle. Let  $n$  be the number of distinct vertices on the circle. Find the sum of the possible values of  $n$ .

*Proposed by Yang Liu*

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