
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 pointing downwards contain two liquids up to certain heights. The radii of the tops of the liquid surfaces are $4$ cm and $8$ cm, respectively. Each cone receives a spherical marble; the first marble has a radius of $2$ cm and the second marble a radius of $1$ cm, both sinking to the bottom, fully submerged without spilling any liquid. Determine the ratio of the rise of the liquid level in the first (narrower) cone to that in the second (wider) cone.
A) 2:1
B) 4:1
C) 6:1
D) 8:1
E) 10:1

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