First off, define "advanced cross."
Second, your F2L should at least be sub-15 seconds before you even think about moving on to a 2 or 3LLL last layer. It would be more beneficial to improve your F2L.
Third, COLL is a waste of time unless you know 2LLL, and if you meant 1L OLL, then PLL is easier to learn and will save more time. If anything, just learn the 8 no edges oriented 1L OLL algs and you'll be fine.
Just practice your F2L a lot, with strategies such as a metronome, putting in the pair blindfolded, and maybe learning some advanced F2L tricks. And for the cross, plot the whole thing out in inspection. The W.H.O.L.E. thing.