
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 hexagon $ABCDEF$ with a side length of $3$ and each internal angle being $120$°. Region $R$ consists of all points inside the hexagon that are closer to vertex $A$ than any of the other five vertices. What is the area of $R$?
A) $\frac{3\sqrt{3}}{2}$
B) $\frac{9\sqrt{3}}{4}$
C) $6\sqrt{3}$
D) $\frac{9\sqrt{3}}{9}$
E) $3\sqrt{3}$

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