
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
Find how many non-similar regular 800-pointed stars are possible, satisfying the given conditions that no three vertices are collinear, all line segments intersect another at a point other than an endpoint, all angles at the vertices are congruent, all line segments are congruent, and the path turns counterclockwise at an angle less than 180 degrees at each vertex.

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