Singular Values & the SVD · Hard problem

The system $x + y = 3$, $y + z = 3$ has infinitely many solutions $(x, y, z)$. The pseudoinverse picks the one of smallest length, $\mathbf x^{+} = A^{+}b$ with $A = \begin{pmatrix}1 & 1 & 0\\0 & 1 & 1\end{pmatrix}$ and $b = \begin{pmatrix}3\\3\end{pmatrix}$. Find $\|\mathbf x^{+}\|^2$.