12. Given two regular tetrahedra $A-O B C$ and $D-O B C$ with their bases coinciding, $M$ and $N$ are the centroids of $\triangle A D C$ and $\triangle B D C$ respectively. Let $\overrightarrow{O A}=\boldsymbol{a}, \overrightarrow{O B}=\boldsymbol{b}, \overrightarrow{O C}=\boldsymbol{c}$. If point $P$ satisfies $\overrightarrow{O P}=x \boldsymbol{a}+y \boldsymbol{b}+z \boldsymbol{c}, \overrightarrow{M P}=2 \overrightarrow{P N}$, then the real numbers $x=$ $\qquad$ ,$y=$ $\qquad$ ,$z=$ $\qquad$ .