
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 \( PQR \), \( \angle R = 90^\circ \), \( PR = 9 \) and \( QR = 12 \). Points \( S \) and \( T \) are on \( \overline{PQ} \) and \( \overline{QR} \), respectively, and \( \angle PTS = 90^\circ \). If \( ST = 6 \), then what is the length of \( ST \)?

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