Let $A_1$ be a midmoint of $BC$, and $G$ is a centroid of the non-isosceles triangle $\triangle ABC$. $GBKL$ and $GCMN$ are the squares lying on the left with respect to rays $GB$ and $GC$ respectively. Let $A_2$ be a midpoint of a segment connecting the centers of the squares $GBKL$ and $GCMN$. Circumcircle of triangle $\triangle A_{1}A_{2}G$ intersects $BC$ at points $A_1$ and $X$. Find $\frac{A_{1}X}{XH}$, where $H$ is a base of altitude $AH$ of the triangle $\triangle ABC$.