
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 right circular cones with vertices facing downwards contain the same amount of liquid. The radii of the tops of the liquid surfaces are \(4\) cm and \(8\) cm respectively. Into each cone is dropped a different spherical marble; the narrow cone receives a marble of radius \(1\) cm, and the wide cone receives a marble of radius \(2\) cm, each sinking to the bottom and being completely submerged without spilling any liquid. What is the ratio of the rise of the liquid level in the narrow cone to the rise in the wide cone?

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