
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 right, circular cone has a height of 10 inches and a radius of 3 inches at the opening. Filling the interior of the cone there is ice cream, capped with a cone (instead of a hemisphere) that has the same radius at the base but a height of 5 inches. Determine the total volume of ice cream.

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