
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 eight spheres, each with a radius of 1, in two layers inside a cylinder. Ensure that each sphere is tangent to its four neighboring spheres, as well as tangent to one base and the lateral surface of the cylinder. Determine the height of the cylinder.

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