
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 plane $P$, there is an isosceles triangle $ABC$ with $|AB| = |BC| = l$ and $|AC| = 2a$. A sphere with radius $r$ touches plane $P$ at point $B$. Two skew lines pass through points $A$ and $C$ and are tangent to the sphere. The angle between each of these lines and plane $P$ is $\alpha$. Find the distance between these lines.

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