
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
Place 8 spheres, each with a radius of 1, into a cylinder in two layers. Ensure that each sphere is tangent to its four neighboring spheres, as well as tangent to one base and the side of the cylinder. Find the height of the cylinder.

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