
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
Quinn makes a festive display by stacking snowballs of radius 4 inches, 6 inches, and 8 inches, plus a smaller ball on top with a radius equal to half of the average radius of the first three snowballs. Assuming all snowballs are perfectly spherical, calculate the total volume of snow used for the display, in cubic inches. Express your answer in terms of $\pi$.

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