In the diagram below, point $A$ is on line segment $\overline{CE}$, and $\overline{AB}$ bisects $\angle DAC$ (meaning that $\overline{AB}$ splits $\angle DAC$ into two congruent angles). If $\overline{DA}\parallel\overline{EF}$ and $\angle AEF = 10 \cdot \angle BAC - 12^\circ$, then what is $\angle DAC$ in degrees?
