In acute triangle \(\triangle ABC,\) the internal angle bisector of \(\angle BAC\) meets \(BC\) at \(D.\) \(E, F\) are the feet of perpendiculars from \(D\) on \(AC, AB\) respectively. Let \(O\) be the circumcenter of \(\triangle AEF.\) Given that \(\angle BAC = 60^{\circ}, \) find \(\angle BAO\) in degrees.

**Details and assumptions**

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