
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 point $E$ inside square $ABCD$ makes $\triangle ABE$ a right triangle with $\angle BAE = 45^\circ$, and the length of each side of the square $ABCD$ is 2, find the area of $\triangle ABF$, where $F$ is the intersection of diagonal $BD$ with line segment $AE$.

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