
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 as follows: in a convex polygon with sides numbered $1, 2, \ldots, n$ (where \(n \geq 6\)), each side $k$ is non-parallel to side $k+3$, and side indices wrap around such that side $n+1$ is side $1$, and so on. When the sides $k$ and $k+3$ of the polygon are prolonged, they intersect. Determine the sum $S$ of the interior angles at the $n$ intersections of these sides.
A) $180^\circ (n - 3)$
B) $180^\circ (n - 4)$
C) $180^\circ (n - 1)$
D) $180^\circ (n - 2)$

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