
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
A lead sphere with a radius of $12 \mathrm{dm}$ is cut by two parallel planes such that the diameter is divided into three equal parts. From the two resulting spherical caps, two equal spheres are formed. From the remaining middle part, a cylindrical tube is made with an inner diameter equal to that of the spheres, and a thickness of $2 \mathrm{~cm}$. What are the diameters of the resulting spheres, and how long is the tube?

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