
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 truncated right circular cone. The truncated cone's top radius is half of its bottom radius. The volume of the truncated cone is thrice that of the sphere. Determine the ratio of the radius of the bottom base to the radius of the top base of the truncated cone.
A) $1.5$
B) $\sqrt{2}$
C) $\sqrt{3}$
D) $2$
E) $\frac{3 + \sqrt{5}}{2}$

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