
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
Rectangle $PQRS$ is inscribed in a semicircle with diameter $\overline{GH}$, such that $PR=20$, and $PG=SH=12$. Determine the area of rectangle $PQRS$.
A) $120\sqrt{6}$
B) $150\sqrt{6}$
C) $160\sqrt{6}$
D) $180\sqrt{6}$
E) $200\sqrt{6}$

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