
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, $r$. If the volume of the cone is one-third that of the sphere, determine the ratio of the altitude of the cone, $h$, to the radius $r$ of its base.
A) $\frac{1}{3}$
B) $\frac{2}{3}$
C) $1$
D) $\frac{4}{3}$
E) $2$

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