
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 triangle $PQR$, $PQ = 18$, $PR = 30$, $QR = 25$, and $PS$ is an angle bisector. Find the ratio of the area of triangle $PQS$ to the area of triangle $PRS$. (Express your answer as a fraction in lowest terms.)

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