
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
A regular polygon with 12 sides is inscribed by six regular polygons of \( n \) sides each so that the vertices of the central polygon touch the centers of the \( n \)-sided polygons. If the sum of the interior angles at every contact point is 360 degrees, what is the value of \( n \)?
A) 6
B) 8
C) 10
D) 12
E) 14

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