
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
Part of an "n-pointed regular star" is depicted. It is a simple closed polygon where all $2n$ edges are congruent, angles $A_1, A_2, \ldots, A_n$ are congruent, and angles $B_1, B_2, \ldots, B_n$ are congruent. If the acute angle at $A_1$ is $15^\circ$ less than the acute angle at $B_1$, and furthermore if the sum of all $A_i$ angles is $180^\circ$ less than the sum of all $B_i$ angles, determine $n$.
A) 10
B) 12
C) 15
D) 18
E) 20

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