
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
A $6 \times 6 \times 6$ cube contains a sphere of radius $3$ and eight smaller spheres of radius $1$. The smaller spheres are each tangent to three faces of the cube and the larger sphere. Determine the minimum size of the cube to contain this configuration.

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