
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 where $n$ is a multiple of 3 and $n \geq 6$, is formed by numbering the sides of a convex polygon consecutively from $1$ to $n$. For each value of $k$, the sides $k$ and $k+3$ (considering indices modulo $n$) are extended until they intersect. Each intersection forms a vertex of the star. Calculate the sum $S$ of the degrees of the interior angles at the $n$ vertices of the star.

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