
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 with a radius of 1, are placed on a horizontal table with each sphere tangential to its neighboring spheres (the centers of the spheres form a square). There is a cube whose bottom face is in contact with the table, and each vertex of the top face of the cube just touches one of the four spheres. Determine the side length of the cube.

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