
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 spheres touch the plane of triangle $ABC$ at points $A$ and $B$ and are located on opposite sides of this plane. The sum of the radii of these spheres is 13, and the distance between their centers is $\sqrt{505}$. The center of a third sphere with radius 8 is located at point $C$, and this sphere touches the first two spheres. Find the radius of the circumcircle of triangle $ABC$.

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