
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 is in the form of an inverted right circular cone. The radius at its base is 10 feet, and its height is 30 feet. The water in the tank fills up 50% of the tank's total capacity. Determine the height of the water in the tank, which can be represented as $a \sqrt[3]{b}$, where $a$ and $b$ are positive integers, and $b$ is not divisible by any perfect cube greater than 1. What is $a+b$?

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