
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
Consider two right circular cones with vertices pointing downwards, each filled with the same amount of water. The radius of the water surface in the first cone is 4 cm, while in the second cone it is 8 cm. A spherical marble with a radius of 2 cm is dropped into each cone, sinking to the bottom and becoming fully submerged without causing any overflow. Determine the ratio of the height increase of the water in the first cone to the increase in the second cone.
A) 1:1
B) 4:1
C) 8:1
D) 2:1

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