
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
Regular polygons with $7, 8, 9,$ and $10$ sides are inscribed in the same circle. No two of these polygons share a vertex, and polygons whose number of sides are consecutive primes do not intersect each other. At how many points inside the circle do two of their sides intersect?
A) 82
B) 88
C) 92
D) 96
E) 100

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