Use the simplex algorithm to solve the problem

$$\max x_{1}+2 x_{2}-6 x_{3}$$

subject to $x_{1}, x_{2} \geqslant 0,\left|x_{3}\right| \leqslant 5$, and

$$\begin{array}{r} x_{1}+x_{2}+x_{3} \leqslant 7 \\ 2 x_{2}+x_{3} \geqslant 1 \end{array}$$