
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 is equal to \(a\). The plane \(\boldsymbol{P}\) passes through vertex \(B\) and the midpoints of edges \(AC\) and \(AD\). A sphere is tangent to the lines \(AB\), \(AC\), and \(AD\), and to the part of plane \(P\) that is inside the tetrahedron. Find the radius of the sphere.

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