
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 $PQR$, $PQ = 17$, $QR = 20$, and $PR = 19$. Point $S$ is on $\overline{QR}$ with $RS = 7$. Point $T$ is on $\overline{QR}$ such that $\angle PQT = \angle SPR$. Find $PT.$

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