
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
An "$n$-pointed star" is created by extending every third side of a convex $n$-sided polygon, labeled consecutively from $1$ to $n$ with $n \geq 6$. The sides $k$ and $k+3$ are extended until they intersect, with indices considered modulo $n$. Determine the degree-sum $S$ of the interior angles at the $n$ points of this newly formed star.
A) $180^\circ (n-1)$
B) $180^\circ (n-2)$
C) $180^\circ (n-3)$
D) $360^\circ$
E) $180^\circ (n-4)$

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