
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
Given the diagram of two circles centered at O, with S on the larger circle, and Q as the point of intersection of OS and the smaller circle, and with PR being a chord of the larger circle tangent to the smaller circle at Q, and OS being the perpendicular bisector of PR, where PR = 12 and QS = 4, find the radius of the larger circle.

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