
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, where $n > 4$, is intersected at each vertex by a smaller regular polygon with $m$ sides, where $m < n$ and $m > 3$. The intersections cause the sides of the larger polygon to be divided, creating new angles at each point of intersection. If each side of the smaller polygon intersects exactly in the middle of each side of the larger polygon, what is the new angle at each point of intersection?
A) $\frac{360}{n} + \frac{(m-2) \times 180}{m}$
B) $\frac{360}{n} - \frac{(m-2) \times 180}{m}$
C) $\frac{180}{n} + \frac{(m-2) \times 360}{m}$
D) $\frac{(n-2) \times 180}{n} - \frac{(m-2) \times 180}{m}$
E) $\frac{(n+m-2) \times 180}{n+m}$

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