
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
Suppose we create a star from a regular polygon with $n$ sides where $n \ge 6$, by marking consecutively the sides $1, 2, \dots, n$, and for each $k$, prolong sides $k$ and $k+3$ until they meet, under the conditions that sides $n+1, n+2, n+3$ correspond respectively to sides $1, 2, 3$. Calculate the sum $S$ of the interior angles at the $n$ points of the star formed.
A) $180^\circ n$
B) $360^\circ$
C) $180^\circ (n+2)$
D) $180^\circ (n-2)$
E) $180^\circ (n-4)$

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