
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 parallelogram $PQRS$, angle $Q$ is trisected by $\overline{QT}$ and $\overline{QU}$, where $T$ is on $\overline{PS}$, $U$ is on $\overline{PR}$, $ST=3$, and $PU=9$. $PQRS$ is a rhombus, and the angle trisected is $120^\circ$. Calculate the area of $PQRS$.

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