
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
Consider a "$n$-pointed complex star" formed as follows: the sides of a convex polygon are numbered consecutively $1,2,\cdots,k,\cdots,n$ for $n \ge 7$. Unlike a typical star, now for all $n$ values of $k$, sides $k$ and $k+3$ are non-parallel and extended to meet after the polygon wraps around (sides $n+1$, $n+2$, and $n+3$ are respectively returned to sides $1$, $2$, and $3$, and so on), effectively intersecting every third side starting from any side numbered $k$. Determine the degree-sum $S$ of the interior angles at the $n$ vertices of this more complex star.
A) $180n$
B) $180(n - 2)$
C) $180(n - 4)$ 
D) $180(n - 6)$

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