
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 an inverted right circular cone. Its base radius is 12 feet, and its height is 60 feet. The water in the tank fills 40% of the tank's capacity. The height of the water in the tank can also be expressed in the form \( a\sqrt[3]{b} \), where \( a \) and \( b \) are integers with \( b \) not divisible by any perfect cube greater than 1. Find \( a + b \).

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