
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 1-inch radius at the opening. The interior of this cone is filled with ice cream. To add more appeal, a hemisphere of ice cream with a 1-inch radius exactly covers the opening of the cone. On top of the hemisphere, there is a smaller cone, with height 2 inches and the same radius that perfectly caps the hemisphere. 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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