
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
How many non-similar regular 300-pointed stars can be created given that:
- A regular \( n \)-pointed star is defined as a union of \( n \) line segments where no three points are collinear and all angles and segments at these points are congruent.
- All vertices of the star are on a regular \( n \)-gon and connected sequentially by skipping \( m \) vertices each time, where \( m \) and \( n \) are relatively prime.
- No regular 3-pointed, 4-pointed, or 6-pointed stars can exist.

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