
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
The height of a cylinder is \(3r\). Inside the cylinder, there are three spheres of radius \(r\), where each sphere touches the other two spheres and the lateral surface of the cylinder. Two spheres touch the bottom base of the cylinder, and the third sphere touches the top base. Find the radius of the base of the cylinder.

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