
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 has created a new larger cup for its dispensers. This larger cup is designed as a right circular cone with a five-inch radius. How tall must the cone be to hold 150 cubic inches of water when filled to its full height? Additionally, determine the volume of water the cup will hold when it is only filled to two-thirds of this height.

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