
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
Given that $BDEF$ is a rectangle and $AB = BC = 1$, find the number of square units in the area of the regular hexagon inside it. The rectangle $BDEF$ is such that $BD = 2 + \sqrt{3}$ and $DE = 2$. Note that each side of the hexagon is equal to $1$.

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