
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 has a base with a radius identical to that of a sphere. The volume of the cone is two-fifths that of the sphere. Determine the ratio of the altitude of the cone to twice the radius of its base.
A) \( \frac{1}{3} \)
B) \( \frac{2}{5} \)
C) \( \frac{3}{5} \)
D) \( \frac{4}{5} \)
E) \( \frac{5}{4} \)

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