
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
Determine how many non-similar regular 1500-pointed stars exist based on the rules that no three vertices are collinear, each segment intersects another, and all segments and angles are congruent with vertices turning counterclockwise at an angle less than 180 degrees at each vertex.

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