
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 $T$ and $U$ trisect $\overline{PS}$, and points $V$ and $W$ trisect $\overline{RQ}$. Rectangle $PQRS$ has side lengths $PS = 6$ and $PR = 3$. If $PT = TU = US$ and $RV = VW = WQ$, find the area of quadrilateral $XYZA$, where $X$, $Y$, $Z$, and $A$ are the midpoints of $\overline{PT}$, $\overline{TU}$, $\overline{US}$, and $\overline{PS}$ respectively.

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