
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 company is designing a larger cup for its new water dispenser. This cup will be a right circular cone with a five-inch radius. What is the minimum height of the cup needed to hold 200 cubic inches of water? The height should be expressed to the nearest whole number.

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