
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
Points $P$, $Q$, $R$, and $S$ lie in the plane of the square $EFGH$ so that $EPF$, $FQG$, $GRH$, and $HSE$ are triangles, where $EPF$ is equilateral, and $FQG$, $GRH$, and $HSE$ are isosceles with the base angles at $Q$, $R$, and $S$, respectively, being $75^\circ$. If $EFGH$ has an area of 36, find the area of $PQRS$.

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