Select all the option$($s$)$ that are correct about K$-$means and EM for Gaussian Mixtures:

$($a$)$ K$-$means and EM always find local optimum.

$($b$)$ The number of clusters of EM and K$-$means both need to be manually set by the user.

$($c$)$ Both EM and K$-$means employ hard assignment.

$($d$)$ K$-$means assumes that the underlying clusters in the data must be distributed according to Gaussian distributions.