
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 1, centered in each of the eight octants and tangent to the coordinate planes, what is the radius of the smallest sphere centered at the origin that contains these eight spheres.

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