
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 sides equal to 4cm. $\overline{QR}$ is extended by half its length to $S$, and $T$ is the midpoint of $\overline{PR}$. Suppose $\overline{TS}$ meets $\overline{PQ}$ at $U$. Find the area of the quadrilateral $QTUS$ in square centimeters.

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