To use compact chainrings you'll have to swap out your crankset so I suggest you just install a triple (The triple/compact debate* is tiresome and a triple set-up will provide the gearing you need and shift just fine - it's a tried and true solution).

*The compact set-up has been around for decades, aka "cyclocross gearing", and works well in some applications, but a triple is still the best option for many folks.