
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 the coordinate plane, 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 $\overline{QR}$ extended at $T$. If
\[
\frac{ST}{SR}=\frac{a}{b},
\]
where $a$ and $b$ are relatively prime positive integers, then determine $a+b$.

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