
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
In a regular polygon of $n = 6$ sides, each side of the polygon is extended such that it intersects with non-sequential extensions, forming a complex geometric shape. If each side is extended infinitely, and the intersections form a secondary internal structure where each vertex of this structure meets three extensions, calculate the angle at these new points.
A) $30^\circ$
B) $45^\circ$
C) $60^\circ$
D) $90^\circ$
E) $120^\circ$

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