
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
Given an inverted cone with base radius $12  \mathrm{cm}$ and height $18  \mathrm{cm}$, and a cylinder with a horizontal base radius of $24  \mathrm{cm}$, calculate the height in centimeters of the water in the cylinder when the cone is full of water and the water is poured into the cylinder.

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