
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
Two tangents  $AT$  and  $BT$  touch a circle at  $A$  and  $B$ , respectively, and meet perpendicularly at  $T$ .  $Q$  is on  $AT$ ,  $S$  is on  $BT$ , and  $R$  is on the circle, so that  $QRST$  is a rectangle with  $QT = 8$  and  $ST = 9$ . Determine the radius of the circle.

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