
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 cyclic quadrilateral $ABCD$, the angles $B$ and $C$ are at adjacent vertices and satisfy $\angle B = \angle C = 3\angle A$. The quadrilateral is such that vertices $B, C$ and $D$ form consecutive vertices of a regular polygon inscribed in the circle. Determine the number of sides $n$ of this regular polygon.
A) 4
B) 8
C) 12
D) 16

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