
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
Vertex $E$ of equilateral $\triangle ABE$ is in the interior of square $ABCD$, and $F$ is the point of intersection of diagonal $BD$ and line segment $AE$. If the length of $AB$ (side of the square) is doubled from the original, to $2\sqrt{1+\sqrt{3}}$, find the area of $\triangle ABF$.
A) $\sqrt{3} - 1$
B) $\sqrt{2}$
C) $2\sqrt{3}$
D) $\sqrt{3}$
E) $\frac{\sqrt{3}}{2}$

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