
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 large water tank in the form of an inverted right circular cone has a radius of its base as 20 feet and a height of 100 feet. The water in the tank occupies $40\%$ of the tank's full capacity. Determine the height of the water in the tank, and express your answer in the form \( a\sqrt[3]{b} \), where \( a \) and \( b \) are positive integers, and \( b \) is not divisible by a perfect cube greater than 1.

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