
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 triangle $\triangle ABC$, medians $\overline{AD}$ and $\overline{BE}$ are perpendicular. Suppose $AD = 18$ and $BE = 24$. Additionally, the angle between side $AC$ and median $AD$ is $30^\circ$. What is the area of $\triangle ABC$?

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