
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
There are two conical tanks, Tank A and Tank B, in a facility. Tank A is an inverted right circular cone with a radius of its base as 20 feet and height as 80 feet. The water in Tank A fills 30% of its capacity. Tank B is upright with a radius of 15 feet and height of 60 feet, and the water fills 50% of its capacity. Determine the height of water in Tank A. The height can be provided in the form $c\sqrt[3]{d}$, where $c$ and $d$ are positive integers, and $d$ is not divisible by a perfect cube greater than 1. What is $c+d$?

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