Given a non-isosceles triangle \(ABC\) with incenter \(I\) and circumcircle \(\omega\). Denote the midpoints of arcs \(BC, AC, AB\) that does not contain the opposite vertex by \(X,Y,Z\) respectively. Denote \(P\) the midpoint of arc \(BC\) containing \(A\). Denote the intersection of \(BP\) and \(ZX\) as \(M\) and the intersection of \(XY\) and \(CP\) as \(N\). Prove that
Quadrilaterals \(BXIM\) and \(XCNI\) are kites.
\(MIN\) are collinear and \(XI\) is perpendicular to \(MN\).