Could well be that new cables & housing will solve the trouble - but we don't know for sure yet. And if this is the problem, an inline barrel-adjuster will solve any slippage with a little twist on the BA. Most especially good for front-derailleurs. The rear can be taken care of with the built-in adjuster on the rear-derailleur - most modern RD's have these.

Cable's loosen after first being installed. This is normal 'cable-stretch' which responds well to a simple tune-up. The rear should be set for a long time after a minor tune-up in the first 100 miles or so. But the front-derailleur - many of them - is fond of being more problematic. Which is where an inline BA comes in handy. Easy to install.

If you have good cable-cutters, this is. Here's an inline BA installed to the FD cable-line: