
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 down contain different amounts of liquid. The radii of the tops of the liquid surfaces are \(4\) cm and \(8\) cm, respectively. Into each cone are dropped two spherical marbles, each of radius \(1\) cm that are completely submerged without spilling any liquid. If initially, the liquid in the narrow cone was twice as deep as that in the wide cone, what is the ratio of the rise of the liquid level in the narrow cone to the rise in the wide cone?
**A)** 1:1  
**B)** 1:2  
**C)** 2:1  
**D)** 4:1

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