
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
Let  $\ell$  be a line and  $P$  be a point in  $\mathbb{R}^3$ . Let  $S$  be the set of points  $X$  such that the distance from  $X$  to  $\ell$  is greater than or equal to two times the distance from  $X$  to  $P$ . If the distance from  $P$  to  $\ell$  is  $d>0$ , find  $\text{Volume}(S)$ .

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