
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, both with vertices facing downwards, initially contain the same volume of liquid. The radii of the tops of the liquid surfaces are 4 cm in the first cone and 8 cm in the second cone. Into each cone is dropped a spherical marble, with the first marble having a radius of 2 cm and the second a radius of 1 cm, both sinking to the bottom and completely submerged without spilling any liquid. Determine the ratio of the rise in the liquid level in the first (narrower) cone to the rise in the second (wider) cone.
A) 1:1
B) 2:1
C) 3:1
D) 4:1
E) 5:1

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