
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 that eight spheres, each with a radius of 2, are placed one in each octant and are each tangent to the coordinate planes, determine the radius of the smallest sphere, centered at the origin, that can fully contain these eight spheres.

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