
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
Given quadrilateral \(ABCD\) satisfies \(\angle ABC = \angle ACD = 90^\circ, AC=18,\) and \(CD=24.\) Diagonals \(\overline{AC}\) and \(\overline{BD}\) intersect at point \(E,\) such that the ratio \(AE:EC = 1:2.\) Calculate the area of quadrilateral \(ABCD\).

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