
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 containing 9 spheres, one of which is tangent to all 6 faces, and the remaining 8 equal spheres tangent to this sphere and three faces of the cube, when viewed directly along one edge, find the distance between the centers of the large and small circles.

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