
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 is shaped like an inverted right circular cone with a base radius of 10 feet and a height of 60 feet. If the water fills $40\%$ of the tank's volume, determine the height of the water in the tank. Express your answer in the form \( c\sqrt[3]{d} \), where \( c \) and \( d \) are integers and \( d \) is not divisible by any cube other than 1. What is \( c+d \)?

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