
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 up contain different amounts of liquid. One cone, labeled A, has a top surface radius for the liquid of 4 cm filled up to a certain height, and cone B has a radius of 8 cm filled to the same vertical height as cone A. A spherical marble of radius 2 cm is dropped into each cone, which sinks to the bottom and is fully submerged without spilling any liquid. Determine the ratio of the rise of the liquid level in cone A to that in cone B.
A) 1:1
B) 1:2
C) 2:1
D) 3:1
E) 4:1

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