
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 XYZ, medians $\overline{XF}$ and $\overline{YG}$ are perpendicular to each other. If $XF = 18$ and $YG = 24$, and the centroid divides each median into segments with a ratio of 3:2 (instead of the usual 2:1), what is the area of $\triangle XYZ$?

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