
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
In a regular "n-pointed double star" polygon, it is constructed by overlapping two congruent n-pointed star polygons such that their vertices interlace. All edges of this double star are congruent, and the angles at vertices $A_1, A_2, \dots, A_n$ in one star are congruent, as are the angles at vertices $B_1, B_2, \dots, B_n$ in the overlapped star, which are congruent among themselves but different from $A_i$ angles. The acute angle at each $A_i$ is $15^\circ$ more than the acute angle at each $B_i$. Determine the minimal number of points $n$ such that these conditions are satisfied.
A) 12
B) 18
C) 24
D) 36
E) 60

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