
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
Let square $XYZW$ have side length $24$. Point $Q$ is located inside the square such that $XQ = 15$ and $YQ = 20$. Consider the centroids of $\triangle{XYZ}$, $\triangle{YZQ}$, $\triangle{ZQW}$, and $\triangle{QWX}$. Assume these centroids form a convex quadrilateral. Determine the area of this quadrilateral.

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