Finding argmax of trace

Question

In my course literature we are trying to find the maximum of the following
$$ \frac{1}{n}tr(Y^TWW^TY) $$ Columns of $W$ are assumed to be orthonormal. So $W^TW=I$.
We factorize $Y$ using SVD and we get $Y=U\Sigma V^T$ (Note that columns of $U, V$ are orthonormal). We are trying to find W that maximizes
$$argmax_{(W)} tr(V\Sigma U^T WW^TU\Sigma V^T)$$ The course literature says that this achieves a maximum when the columns of $W$ are collinear with the columns of $U$ that are associated with the $k$ largest singular values of $\Sigma$. That is, $W=U_k$.

My attempt: $$ \text{Using cyclical property of trace} \\ tr(V\Sigma U^T WW^TU\Sigma V^T)=tr(U\Sigma V^TV\Sigma U^T WW^T)\\ =tr(U\Sigma^2U^TWW^T) $$ However I do not understand where to go from here or what two matrices having collinear columns means. Any help is appreciated.