
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
Equilateral $\triangle ABC$ has side length $2$ and equilateral triangles are constructed on each side lying outside the triangle with their bases as each side of the triangle. Determine the area of the hexagon formed by the vertices of these triangles opposite their respective bases.
A) $4\sqrt{3} - 3$
B) $4\sqrt{3}$
C) $\frac{12 + 3\sqrt{3}}{4}$
D) $4\sqrt{3} + 3$
E) $3\sqrt{3} - 4$

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