
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
The edge of a regular tetrahedron \(ABCD\) is \(a\), point \(K\) is the midpoint of edge \(AB\), point \(E\) lies on edge \(CD\) and \(EC: ED = 1: 2\), point \(F\) is the center of face \(ABC\). Find the angle between lines \(BC\) and \(KE\), the distance between these lines, and the radius of the sphere passing through points \(A\), \(B\), \(E\), and \(F\).

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