
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
Circles centered at $P$ and $Q$ each have radius 3. Point $R$ is the midpoint of $\overline{PQ}$, and $PR=3\sqrt{3}$. Segments $RS$ and $RT$ are tangent to the circles centered at $P$ and $Q$, respectively, and $\overline{GH}$ is a common tangent. What is the area of the shaded region $RSGHT$?

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