
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 regular star polygon with $n$ points. Each point of the star has two angles associated with it: one at $C_i$ and one at $D_i$ for $i = 1, 2, \ldots, n$. All $C_i$ angles are congruent, and all $D_i$ angles are congruent. If the acute angle at each $C_i$ is $15^\circ$ less than the acute angle at each $D_i$, determine the value of $n$.
A) 12
B) 18
C) 24
D) 36
E) 60

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