
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 ceiling design features a decorative "n-pointed regular star". Each of the star's points has two sorts of angles alternating: one sharp (denoted as $A_i$ for $i=1, 2, \ldots, n$ which are all congruent), and one wider (denoted as $B_i$ for $i=1, 2, \ldots, n$ which are also congruent). It is known that each angle at $A_i$ is $20^\circ$ less than the corresponding angle at $B_i$. Determine the possible number of points $n$ in this star.
A) 9
B) 12
C) 18
D) 24
E) 36

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