
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 a cube with side length 2 and 8 congruent spheres inside it, where one sphere has its center at the center of the cube and each of the others is tangent to this center sphere and to only one face of the cube, find the radius of each sphere.

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