
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
Given triangle $PQR$, we have $PQ = 30$, $QR = 50$, and $PR = 54$. Points $S$ and $T$ are on $PQ$ and $PR$ respectively, with $PS = 18$ and $PT = 24$. Calculate the ratio of the area of triangle $PST$ to the area of the quadrilateral $QRST$.

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