
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 right circular cone and a sphere share the same base radius, $r$. The volume of the cone is one-third of the volume of the sphere. Calculate the ratio of the altitude of the cone to the radius of its base.
A) $\frac{1}{1}$
B) $\frac{1}{2}$
C) $\frac{4}{3}$
D) $\frac{2}{1}$
E) $\sqrt{\frac{5}{4}}$

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