
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 isosceles $\triangle ABC$ where $AB = AC = 2$ and $BC = 1$, equilateral triangles $ABD$, $BCE$, and $CAF$ are constructed outside the triangle. Calculate the area of polygon $DEF$.
A) $3\sqrt{3} - \sqrt{3.75}$
B) $3\sqrt{3} + \sqrt{3.75}$
C) $2\sqrt{3} - \sqrt{3.75}$
D) $2\sqrt{3} + \sqrt{3.75}$

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