If it's not six, then it must be

Geometry Level 3

Consider a triangle \(ABC\) and \(M\) the middle of the segment \(BC\). Let the angle bisector of angle \(AMB\) intersect side \(AB\) at a point \(E\) and the angle bisector of angle \(AMC\) intersect side \(AC\) at a point \(F\). If \(AB=15, MC=5\) and \(AC=12\), find the integer value of the perimeter of the triangle \(AEF\).

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