
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
Eight spheres of radius 2 are each tangent to the faces of an inner cube centered at the origin, with each sphere located in one of the octants, and the side length of the cube is 6. Find the radius of the smallest sphere, centered at the origin, that encloses these eight spheres.

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