
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 $PQRS$, side $PQ$ measures $8$ units and side $QR$ measures $4$ units. Points $T$ and $U$ are on side $RS$ with segment $RT$ measuring $2$ units and segment $US$ measuring $3$ units, and lines $PT$ and $QU$ intersect at $V$. What is the area of triangle $PVQ$?

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