
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 conical flasks have vertices facing down and initially contain equal volumes of liquid. The radii of the liquid surfaces at the top are $4$ cm and $8$ cm. A spherical marble with a radius of $2$ cm is dropped into each flask, sinking fully without causing any liquid to spill. Calculate the ratio of the increase in the liquid level height in the narrower flask to that in the wider flask.
A) 1:1
B) 3:1
C) 2:1
D) 5:1
E) 4:1

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