
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
A regular polygon of $n$ sides, where $n \geq 7$, is used to form three smaller identical stars by extending alternating sets of sides internally. Calculate the angle at each point where the sides intersect inside each of these stars.
A) $\frac{180(n-2)}{n}$ 
B) $\frac{180n}{n+2}$
C) $\frac{180(n-6)}{n}$
D) $\frac{360(n-6)}{n}$
E) $\frac{180n}{7n}$

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