
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
A sphere intersects the xy-plane in a circle centered at $(1,3,0)$ with a radius of 2. The sphere also intersects the yz-plane in a circle centered at $(0,3,-8),$ with radius $r.$ Find $r$ and verify the radius of the sphere.

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