
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 convex polygon has $n$ sides, where $n \ge 6$. For each side $k$ of the polygon (numbered $1, 2, ..., n$), extend sides $k$ and $k+3$ (considering indices modulo $n$) to form an intersecting point outside the polygon. These intersections form a new geometric shape called an "$n$-extended star". If $S$ represents the sum of the interior angles at the $n$ points of this $n$-extended star, what is $S$?
A) $180^\circ (n-3)$
B) $180^\circ (n-2)$
C) $360^\circ$
D) $180^\circ n$

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