
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 cylindrical water tank has a radius of 20 feet and a height of 100 feet. It is filled with water to a height that is $30\%$ of the tank's total capacity. The height of the water in the tank can be written 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}
user