
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
Fifteen points are marked on a circle. How many distinct convex polygons of four or more sides can be drawn using some (or all) of the fifteen points as vertices, discounting any subset of points that lie on the same semicircle?

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