
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
Given two right circular cones with the same volume and vertices pointing down, with base radii of 4 cm and 8 cm for the narrower and wider cones, respectively. Two spherical marbles with radii 2 cm and 1 cm are dropped into the narrow and wide cone, fully submerging without spilling any liquid. Find the ratio of the increase in the water level in the narrow cone to the increase in the water level in the wide cone.

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