
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 $P$, $Q$, $R$, $S$, $T$, and $U$ lie in the plane of regular hexagon $ABCDEF$ such that $APB$, $BQC$, $CRD$, $DSE$, $ETF$, and $FUA$ are equilateral triangles. If $ABCDEF$ has an area of 54, find the area of $PQRSTU$. Express your answer in simplest radical form.

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