
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 water tank in the diagram below is in the shape of an inverted right circular cone. The radius of its base is 20 feet, and its height is 60 feet. The water in the tank fills $40\%$ of the tank's capacity. Find the height of the water in the tank, given that it can be expressed as $a\sqrt[3]{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by a perfect cube greater than 1. What is $a+b$?

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