
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 10 inches tall with a 1.5-inch radius at the opening. Above this cone sits a cylindrical scoop of ice cream with the same radius as the cone's opening and a height of 2 inches. A hemisphere of ice cream, matching the radius of the cylinder and the cone's opening, neatly caps off the entire structure. Calculate the total volume of ice cream in terms of $\pi$.

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