
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, one per octant, each have radius 2 and are tangent to the coordinate planes. What is the radius of the smallest sphere, centered at the origin, that contains these eight spheres?
A) \(2 + \sqrt{3}\)
B) \(2\sqrt{3} + 2\)
C) \(\sqrt{12} + 4\)
D) \(\sqrt{15}\)

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