
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, $\angle C = 90^\circ$, $\overline{AD} = \overline{DB}$, $DE \perp AB$, $\overline{AB} = 24$ and $\overline{AC} = 10$. Let $F$ be a point on $\overline{AC}$ such that $\overline{AF} = \overline{FC}$. Calculate the area of quadrilateral $ADEF$.
A) $10\sqrt{119} - \frac{360}{\sqrt{119}}$
B) $5\sqrt{119} - \frac{180}{\sqrt{119}}$
C) $20\sqrt{119} - \frac{720}{\sqrt{119}}$
D) $\frac{970}{\sqrt{119}}$

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