
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
Triangle \(PQR\) has a right angle at \(Q\), \(PQ=5\) and \(QR=12\). Triangle \(PRS\) has a right angle at \(P\) and \(PS=20\). Points \(Q\) and \(S\) are on opposite sides of \(\overline{PR}\). The line through \(S\) parallel to \(\overline{PQ}\) meets \(\overline{RQ}\) extended at \(T\). If
\[
\frac{ST}{SR} = \frac{u}{v},
\]
where \(u\) and \(v\) are relatively prime positive integers, then \(u+v=\)

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