
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
There are two right circular cones with vertices pointing downwards, each containing the same volume of liquid. The radii of the surfaces of the liquids are 4 cm and 8 cm. One spherical marble with radius 2 cm is dropped into the smaller cone, and another spherical marble with radius 1 cm is dropped into the larger cone. Each marble sinks to the bottom and is completely submerged without spilling any liquid. Calculate the ratio of the rise of the liquid level in the smaller cone to the rise in the larger cone.

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