Let \[ A(t)=\begin{pmatrix} t & 1 & 1\\ 1 & t & 1\\ 1 & 1 & t \end{pmatrix},\qquad b=\begin{pmatrix}1\\0\\0\end{pmatrix}. \] Consider the system \(A(t)x=b\). For which real values of \(t\) does the system have at least one solution?