
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, one with a base radius of 4 cm and the other with a base radius of 8 cm, have the same initial height of liquid, such that the surface areas of the liquid in both cones are equal. A spherical marble of radius 1 cm, which sinks to the bottom and is completely submerged without spilling any liquid, is dropped into each cone. Determine the ratio of the rise of the liquid level in the smaller cone to the rise in the larger cone.
A) 1:1
B) 2:1
C) 4:1
D) 8:1

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