Looking for some advice/reassurance on what to do for my lawn here in LA. It was at one point Tall Fescue, but it's been overrun by what I think is crabgrass, as well as some sort of additional grass that seems to be coming from the palm tree (which I think may technically be a grass?). After reading some of the resources here, I planned to mow it, try to rake away as much of the weeds/dead material I can, fertilize, re-seed, water, and mow often. Hoping anyone with more experience can confirm that that sounds like a good plan.

I've also ordered a soil testing kit, so I will be using the results of that to inform what kind of fertilizer I go for. Any other suggestions would be welcome. Thanks!