For a symmetric, positive definite matrix $A$ with the spectral radius $\rho(A)$, the linear system $A x=b$ is solved by the iterative procedure

$$x^{(k+1)}=x^{(k)}-\tau\left(A x^{(k)}-b\right), \quad k \geq 0$$

where $\tau$ is a real parameter. Find the range of $\tau$ that guarantees convergence of $x^{(k)}$ to the exact solution for any choice of $x^{(0)}$.