Two points M, N isogonals with respect two triangles ABC and A'B'C'

1) The reflections of the lines AA', BB', CC' on the A-bisector cut the sides of A'B'C' at three points collinear in LA.
2) Let NA be the Newton line of the quadrilateral formed by La and the sides of A'B'C'.
3) Draw analogously NA'.
4) The lines Na and NA' intersect at Q.
5) There are two conics with center Q inscribed in ABC and A'B'C'. Their focii are the requested points M, N.