The position vectors of the point $A, B$ are $\mathbf{a}, \mathbf{b}$ respectively. If the position vector of the point $C$ is $\frac{a}{2}+\frac{b}{3}$, then

If $|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{a}-\mathbf{b}|^2+|\mathbf{a}+2 \mathbf{b}|^2=20$, then $(a, b)=$