
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 of radius 1 are pairwise tangent. Find the height of a cylinder containing these spheres such that three of them touch one base and the lateral surface, and the fourth touches the other base of the cylinder.

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