
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 $\mathbf{ABCD}$ fulfills conditions $\angle ABC = \angle ACD = 90^{\circ}$, with $AC = 24$ and $CD = 18$. Point $E$ is the intersection of diagonals $\overline{AC}$ and $\overline{BD}$, with $AE = 6$. Determine the area of quadrilateral $\mathbf{ABCD}$.
A) 486
B) 504
C) 520
D) 540

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