
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 right triangle $PQR$, $PQ=12$, $QR=16$, and $\angle Q = 90^\circ$. Points $S$ and $T$ are on $\overline{PQ}$ and $\overline{PR}$ respectively, such that $PS = \frac{2}{3} \times PQ$ and $PT = \frac{2}{3} \times PR$. Lines $\overline{RT}$ and $\overline{QS}$ intersect at point $U$. Compute the ratio of the area of quadrilateral $PUTS$ to the area of triangle $QUV$, where $V$ is the midpoint of $\overline{QR}$.

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