Orthogonality & Least Squares · Challenge problem

An $m\times2$ matrix $A$ has orthonormal columns, and $A^T\mathbf b = (3,4)$ for a vector $\mathbf b$ with $\|\mathbf b\|=6$. Find the minimum possible value of $\|A\mathbf x-\mathbf b\|^2$ over all $\mathbf x$.