
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 circle circumscribed around a star-polygon with $n$ points, where $n>4$. Each internal angle of the star-polygon can be calculated as $\frac{180(n-4)}{n}$ degrees. If each point of the star-polygon touches the circle, what is the measure in degrees of the angle at each intersection point outside the star-polygon where two lines extending from adjacent points intersect?
A) $\frac{180(n-4)}{n}$
B) $\frac{360(n-4)}{n}$
C) $\frac{720}{n}$
D) $\frac{360(n-2)}{n}$
E) $\frac{180(n-2)}{n}$

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