
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
In a space, let  $B$  be a sphere (including the inside) with radius of 1. Line  $l$  intersects with  $B$ , the length of the common part is the line segment with the length of  $\sqrt{3}$ .

(1) Find the distance between the center of  $B$  and  $l$ .

(2) Find the volume of the solid generated by rotating  $B$  about  $l$ .

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