
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
On a horizontal table surface $\alpha$, there are 4 spheres each with a radius of $2R$, and adjacent spheres are tangent to each other (the lines connecting the centers of the spheres form a square). A smaller sphere with a radius of $R$ is placed on top of these 4 spheres, and it is just tangent to the 4 spheres below. The distance from the center of the small sphere to the horizontal table surface $\alpha$ is __________.

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