
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
Square $WXYZ$ has a side length of $40$. Point $Q$ is inside the square so that $WQ = 15$ and $XQ = 35$. The centroids of triangles $\triangle{WXQ}$, $\triangle{XZQ}$, $\triangle{ZYQ}$, and $\triangle{YWQ}$ form the vertices of another convex quadrilateral. Calculate the area of this quadrilateral.

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