
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
$PQR$ is an equilateral triangle with each side of length 4 cm. $\overline{QR}$ is extended by 50% of its own length to point $S$, and $T$ is the midpoint of $\overline{PQ}$. Suppose $\overline{TS}$ meets $\overline{PR}$ at point $U$. Find the area of the quadrilateral $QTUR$.

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