
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 opposite directions contain the same volume of liquid. The radii of the liquid surfaces in the first (narrow) and second (wide) cone are \(4\) cm and \(8\) cm, respectively. A spherical marble of radius \(2\) cm is dropped into the first cone, and a spherical marble of radius \(1\) cm is dropped into the second cone; both marbles are completely submerged without spilling any liquid. Determine the ratio of the rise of the liquid level in the narrow cone to the rise of the liquid level in the wide cone.
A) 8:1
B) 4:1
C) 2:1
D) 10:1
E) 8.156:1

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