
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
In the diagram, $\angle FAB$ and $\angle ABC$ are right angles, $AB=5,$ $BC=3,$ $AF=7,$ and $\overline{AC}$ and $\overline{BF}$ intersect at $D.$ What is the difference between the areas of $\triangle ADF$ and $\triangle BDC?$

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