
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 rectangle $PQRS$, angle $R$ is trisected by $\overline{RG}$ and $\overline{RH}$, where $H$ is on $\overline{PQ}$, $G$ is on $\overline{PS}$, $PH=8$, and $SG=4$. Find the area of $PQRS$.

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