
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 "$n$-pointed advanced star" is formed as follows: in a convex polygon with sides numbered consecutively $1,2,\dots,n$, where $n\geq 5$, sides $k$ and $k+3$ are non-parallel for all $k$, with side indices taken modulo $n$. Extend the $n$ pairs of sides numbered $k$ and $k+3$ until they meet. Determine the degree-sum of the interior angles at the $n$ points of this advanced star.
A) $180^\circ$ 
B) $360^\circ$ 
C) $180(n+2)^\circ$
D) $180(n-2)^\circ$ 
E) $180(n-4)^\circ$

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