
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 defined by alternate congruent angles, as known components of its structure. Each point of this star has angles $A_1,A_2,\ldots,A_n$ and $B_1,B_2,\ldots,B_n$ that are congruent to their respective groups. If the acute angle at each $A_i$ is $15^\circ$ more than the acute at each $B_i$, how many points does the star have?
A) 12
B) 18
C) 24
D) 36
E) 60

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