
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
Square $PQRS$ has an area of 36, and points $U$, $V$, $W$, and $X$ are placed such that $PUQ$, $QVR$, $RWS$, and $SXP$ are equilateral triangles. Each triangle is located externally at alternate vertices of square $PQRS$. Find the area of quadrilateral $UVWX$.

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