
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 the radii of the tops of the liquid surfaces are 5 cm and 10 cm, and the radius of the spherical marble is 2 cm, determine the ratio of the rise of the liquid level in the narrower cone to the rise of the liquid level in the wider cone.

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