
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 $ABCD$ has mid-segments $EF$ and $GH$ such that $EF$ goes from midpoint of $AB$ to midpoint of $CD$, and $GH$ from midpoint of $BC$ to midpoint of $AD$. Given that $EF$ and $GH$ are perpendicular, and the lengths are $EF = 18$ and $GH = 24$, find the area of $ABCD$.

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