
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 cone with base radius $15 \mathrm{cm}$ and height $20 \mathrm{cm}$ is full of water. This water is then poured into another cone with a base radius of $10 \mathrm{cm}$ and a height of $15 \mathrm{cm}$, which already contains water filled up to a height of $9 \mathrm{cm}$. The water that overflows is collected into a cylindrical container with a radius of $6 \mathrm{cm}$. Determine the height of the water in the cylindrical container.

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