
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 identical volumes of liquid. The radii of the liquid surfaces' tops are $5$ cm and $10$ cm respectively. A spherical marble with a radius of $2$ cm is dropped into each cone. Each marble sinks completely to the bottom without spilling any liquid. 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) 2:1
C) 3:1
D) 4:1
E) 5:1

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