2. As shown in the figure, in $\triangle A B C$, point $O$ is the midpoint of $B C$, a line through point $O$ intersects lines $A B$ and $A C$ at two different points $M$ and $N$, respectively. If $\overrightarrow{A B}=m \overrightarrow{A M}, \overrightarrow{A C}=$ $n \overrightarrow{A N}$, then the value of $m+n$ is $\qquad$.
2. 2 Detailed Explanation: $\overrightarrow{A O}=\frac{1}{2} \overrightarrow{A B}+\frac{1}{2} \overrightarrow{A C}=\frac{m}{2} \overrightarrow{A M}+\frac{n}{2} \overrightarrow{A N}$, since $M, O, N$ are collinear, we have $\frac{m}{2}+\frac{n}{2}=1, m+n=2$.