
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
A cube with sides 1 meter in length is filled with water and has a tiny hole through which the water drains into a cylinder of radius 1 meter. If the water level in the cube is falling at a rate of 1 centimeter per second, at what rate is the water level in the cylinder rising?

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