Just like Jake says. I played pianoteq with Asio4all too years ago, but an external soundcard sounds better (you have a newer laptop of course, so might see for yourself how the difference is for you, maybe some friend can lend you an external usb card?).
Active monitors are very fine too, but of course it depends upon where you live, if you can play loud over monitors all the time or if some neighbours want silence etc. (like funnily enough in Germany more and more younger neighbours, hmm....20-30 is the new 90?^^).
What I like as a workaround against neighbours^^ is to sometimes use a plugin like Redline monitor or Toneboosters Isone. Those plugins mainly narrow the stereo image. You would never use those if you play over monitors, but they are quite good when you have to mix songs on headphones, for example. It is a "second best" idea if you rely on headphones. You can test the redline plugin 2 months for free, whereas that from Toneboosters was very cheap, 20 Euro I think it was, and there is also a demo. So I just thought I'd mention that, you could test for yourself and see if you like it if you would not buy monitors - which are great, but can be expensive.
But a nice external soundcard would surely be the first I'd think about. I use a Steinberg UR 22 usb card and am happy with that, but there are a lot of soundcards out there for your laptop, so you might read around and go to a good shop for that.