
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 the horizontal surface $\alpha$, there are 4 balls with radii of $2R$, and adjacent balls are tangent to each other (the line connecting the centers of the balls forms a square). On top of these 4 balls, there is a small ball with a radius of $R$, which is tangent to all 4 balls below. Calculate the distance from the center of the small ball to the horizontal surface $\alpha$.

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