
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
If two circles touch at P, and QP and SU are perpendicular diameters of the larger circle that intersect at O, point V is on QP and VP is a diameter of the smaller circle, and the smaller circle intersects SU at T, and QV = 9 and ST = 5, find the sum of the lengths of the diameters of the two circles.

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