
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
Two cones, one right circular cone with its vertex facing down and another with its vertex facing up, have the same height and their vertices aligned at the same point. The lower cone's radius is 4 cm at the top of the liquid, which is 8 cm below the vertex. The upper cone's radius is 8 cm at its bottom, filled with the same volume of liquid lying 8 cm above the vertex. A spherical marble of radius 2 cm is dropped into each cone, which sinks to the bottom in the lower cone and sinks to the "bottom" now the vertex region in the upper cone without spilling any liquid. What is the ratio of the rise of the liquid level in the lower cone to the rise of the liquid level in the upper cone?
A) 3:1
B) 3.5:1
C) 4:1
D) 3.67:1
E) 5:1

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