
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 right triangle \(PQR\), a circle is constructed on the leg \(PR\) as its diameter, which intersects the hypotenuse \(PQ\) at point \(T\). A tangent to the circle is drawn through point \(T\), and it intersects the leg \(RQ\) at point \(S\). Find the length of \(SQ\) if \(PT = 15\) and \(QT = 5\).

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