
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 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. Additionally, a cylindrical layer of ice cream is placed on top of the hemisphere, with the same radius as the hemisphere and a height of 2 inches. Calculate the total volume of ice cream. Express your answer in terms of $\pi$.

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