
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 plane, four spheres of radius \( 22 - 11 \sqrt{2} \) are touching each other, and their centers form a square. Above the center of the square, on top of the four spheres, a fifth sphere of the same radius is placed. Find the distance from its highest point to the plane.

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