
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 $4, 6,$ and $8$ sides are inscribed in the same circle. At most one vertex may be shared between any two of the polygons, and no three of their sides intersect at a common point. At how many points inside the circle do two (not the same) of their sides intersect?
A) 142
B) 160
C) 164
D) 168
E) 172

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