
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
Four spheres each of radius 2 are arranged such that each sphere is tangent to the other three spheres. These spheres are symmetrically placed around the origin. Find the radius of the smallest sphere, centered at the origin.

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