Use the two-phase simplex method to solve the problem

$$\begin{array}{llllll} \operatorname{minimize} & 5 x_{1}-12 x_{2}+13 x_{3} & & \\ \text { subject to } & 4 x_{1}+5 x_{2} & & \leq & 9 \\ & 6 x_{1}+4 x_{2}+ & x_{3} & \geq & 12 \\ & 3 x_{1}+2 x_{2}-x_{3} & \leq & 3 \\ & x_{i} \geq 0, & i=1,2,3 \end{array}$$