
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
We fill a cone (held with its vertex downwards) with water, so that the water stands at a height of $10 \mathrm{~cm}$. When the cone is sealed at the opening and flipped to stand on its base, the water now stands at a height of $2 \mathrm{~cm}$. What is the height of the cone?

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