
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 volume of the solid of revolution \( V_1 \) obtained by rotating the region bounded by the curves \( x^2 = 4y \), \( x^2 = -4y \), \( x = 4 \), and \( x = -4 \) about the y-axis is calculated. The volume of the solid of revolution \( V_2 \) obtained by rotating the region defined by \( x^2 + y^2 \leqslant 16 \), \( x^2 + (y-2)^2 \geqslant 4 \), \( x^2 + (y+2)^2 \geqslant 4 \) about the y-axis is also calculated. Determine the relationship between \( V_1 \) and \( V_2 \).

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