
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 interior of a right, circular cone is 12 inches tall with a 3-inch radius at the opening. The interior of the cone is filled with ice cream, and the cone has a hemisphere of ice cream exactly covering the opening of the cone. On top of the hemisphere, an additional cylindrical layer of ice cream is added that has the same radius as the hemisphere and a height of 2 inches. What is the total volume of the ice cream? Express your answer in terms of $\pi$.

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