
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 obtained by rotating the region bounded by the curves \( x^{2}=4y, x^{2}=-4y, x=4, x=-4 \) around the \( y \)-axis is \( V_{1} \). The volume of the solid obtained by rotating the region defined by \( x^{2}y^{2} \leq 16, x^{2}+(y-2)^{2} \geq 4, x^{2}+(y+2)^{2} \geq 4 \) around the \( y \)-axis is \( V_{2} \). Determine the relationship between \( V_{1} \) and \( V_{2} \).

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