
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 rectangle $PQRS$, points $M$ and $N$ trisect $\overline{PQ}$, and points $T$ and $U$ trisect $\overline{SR}$. $PS = QN = 3$. Quadrilateral $WXYZ$, with vertices at the midpoints of $MT$, $NU$, $\overline{PQ}$, and $\overline{SR}$ respectively, is present within this geometrical arrangement. Determine the area of quadrilateral $WXYZ$.

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