
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 upwards contain equal volumes of liquid. The radii of the surfaces where cones are filled with liquid are \(4\) cm and \(8\) cm. A spherical marble of radius \(2\) cm is gently dropped into each, sinking to the bottom, completely submerged without overflowing. Determine the ratio of the liquid level rise in the cone with the smaller initial radius to that in the cone with the larger radius.
A) 1:1
B) 2:1
C) 3:1
D) 4:1
E) 5:1

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