
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
Given mobile points  $P(0,\ \sin \theta),\ Q(8\cos \theta,\ 0)\ \left(0\leq \theta \leq \frac{\pi}{2}\right)$  on the  $x$ - $y$  plane.
Denote by  $D$  the part in which line segment  $PQ$  sweeps. Find the volume  $V$  generated by a rotation of  $D$  around the  $x$ -axis.

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