
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
The radius of a sphere is $r$ units, the radius of a hemisphere is $3r$ units, and the height of a cone is $2r$ units with the same radius as the sphere. What is the ratio of the volume of the sphere to the combined volume of the hemisphere and the cone?

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