Seja o sistema:$$\{\begin{array}{l}3x_1^2+3x_2^2+3x_3^2=6x_1-1\\ 3x_1^2+3x_2^2+3x_4^2=6x_3-1\\ 3x_1^2+3x_3^2+3x_4^2=6x_2-1\\ 3x_2^2+3x_3^2+3x_4^2=6x_1-1\end{array}$$O valor de $\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}+\frac{1}{x_4}$ é: