
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 height of 100 units and a base radius of 50 units. It is sliced into three pieces by planes parallel to its base, where the topmost segment is 20 units tall, the middle segment is 30 units tall, and the bottom segment is 50 units tall. What is the ratio of the volume of the middle segment to the volume of the bottom segment?

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