
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 is centered at a point with integer coordinates and passes through the three points \((2,0,0)\), \((0,4,0)\), and \((0,0,6)\), but not the origin \((0,0,0)\). If \(r\) is the smallest possible radius of the sphere, compute \(r^{2}\).

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