
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 sphere is inscribed in a right circular cylinder such that the diameter of the sphere is equal to the diameter of the cylinder. Given that the volume of the cylinder is twice that of the sphere, find the ratio of the height of the cylinder to the diameter of the sphere.
A) $\frac{3}{2}$
B) $\frac{4}{3}$
C) 2
D) $\frac{5}{3}$

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