
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
For an "$n$-pointed star" formed from a convex polygon where each side of the polygon is labeled consecutively from $1$ to $n$ and $n \ge 5$, determine the degree-sum, $S$, of the interior angles at the $n$ vertices of the star-shaped polygon thus obtained.

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