
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
Points \(A\) and \(B\) are taken on the side of an angle with vertex \(O\) (\(A\) is between \(O\) and \(B\)), and \(OA = 3 \cdot AB\). A circle passing through points \(A\) and \(B\) touches the other side of the angle at point \(D\). Point \(E\) is taken on the ray \(OD\) (with \(D\) between \(O\) and \(E\)). It is known that \(OE = m\), \(\angle BOE = \alpha\), and \(\angle BEO = \beta\). Find the radius of the circle.

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