
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 $4, 5, 6,$ and $7$ sides are inscribed in the same circle. Each polygon does not share a vertex with any other polygon, and at most two polygons intersect at any one point inside the circle. How many points inside the circle do exactly two sides from different polygons intersect?
A) 52  
B) 56  
C) 60  
D) 64  
E) 68

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