
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 right $\triangle ABE$ (where $\angle AEB = 90^\circ$) lies on the diagonal $AC$ of square $ABCD$, and $F$ is the point of intersection of diagonal $BD$ and line segment $AE$. The side length of square $ABCD$ is 2. Determine the area of $\triangle ABF$.
A) 0.5  
B) 1  
C) 1.5  
D) 2

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