
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 cone is filled with water. Two solid spheres are placed in the cone as shown. The spheres are touching each other, each sphere touches the cone all the way around, and the top of the top sphere is level with the top of the cone. The larger sphere has a radius twice that of the smaller sphere. If the volume of the water remaining in the cone is \(2016 \pi\), determine the radius of the smaller sphere.

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