
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 $PQR$, which is a right triangle with legs $PQ$ and $PR$, points $S$ and $T$ lie on $PQ$ and $PR$ respectively, such that $PS:SQ = PT:TR = 1:3$. If $QT = 20$ units, and $SR = 35$ units, what is the length of hypotenuse $QR$? Express your answer in simplest radical form.

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