
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 water tank is shaped like an inverted right circular cone. The radius of its base is 20 feet, and its height is 100 feet. The water in the tank fills 20% of the tank's capacity. The height of the water in the tank can be expressed as \( c\sqrt[3]{d} \), 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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