
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
The volume of water in the inverted cone is equal to the volume of the cylinder, and can be calculated using the formula $\frac{1}{3}\pi r^2 h$ where $r$ and $h$ are the radius and height of the cone. 

Given that the water from the cone fully fills the cylinder, the volume of water in the cone is equal to the volume of the cylinder, which is $\pi R^2 h$, where $R$ is the radius and $h$ is the height in the cylinder.

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