
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 with a right angle at R, PR = 5 and RQ = 12. Triangle PQS has a right angle at P, and PS = 15. Points R and S are on opposite sides of line PQ. The line through S parallel to line PR meets line RQ extended at T. Calculate the ratio $\frac{ST}{SQ}$, where the answer should be expressed as a sum of relatively prime positive integers.

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