
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
Quadrilateral $ABCD$ is a square, and segment $AF$ is perpendicular to segment $FD$. Let $AF = 4$ units and $FD = 3$ units. Given that $AF$ and $FD$ intersect at their midpoint $F$ which is shifted from point $A$ along the diagonal $AC$ of the square. Compute the area of pentagon $AFDCB$, in square units.

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