
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 with $n$ sides ($n > 4$) is used to create a modified star by extending every alternate side. Calculate the angle formed at each vertex of the resulting geometric shape?
**A)** $\frac{180(n-2)}{n}$  
**B)** $\frac{180(n-4)}{n}$  
**C)** $\frac{360(n-4)}{n}$  
**D)** $180 - \frac{90(n-4)}{n}$  
**E)** $\frac{360}{n}$

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