
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
Compute the volume of the solid formed by rotating the region bounded by the following curves around specified axes:

1) \( y^{2} = 2px \), \( x = a \) around the \( O x \)-axis;
2) \( \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \) around the \( O y \)-axis;
3) \( 2y = x^{2} \), \( 2x + 2y - 3 = 0 \) around the \( O x \)-axis;
4) \( x = a \cos^{3} t \), \( y = a \sin^{3} t \) around the \( O x \)-axis;
5) \( y = 4 - x^{2} \), \( y = 0 \) around the line \( x = 3 \).

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