
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
Let square $ABCD$ be positioned on a coordinate plane with $A$ at the origin (0,0) and $B$ at $(2,0)$, making the side length of the square 2 units. Inside the square, place point $E$ such that triangle $ABE$ is equilateral, with $E$ inside the square. Let $F$ be the point of intersection between diagonal $BD$ and line segment $AE$. Compute the area of triangle $ABF$.
A) $\sqrt{3}$
B) $2\sqrt{3} - 2$
C) $2\sqrt{3} - 3$
D) $2\sqrt{3} - 4$

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