And does your Cary integrated amp have Left/Right preouts?
If so, then run a sub cable from your Marantz to the LFE input on your sub and run 2 sub cables from the L/R preouts on the Cary to the Left/Right inputs on your sub.
When you watch movies, the Marantz will send LFE signals to your sub and the Cary will be in HT Bypass (so the preamp section is bypassed and it is nothing more than a power amp in this mode, so no bass signals will be coming out of the preouts). Your Marantz will apply any bass management to the sub.
When you listen to music, turn off the Marantz (or mute it), and select your source device to listen to and the Cary will send signals via the preouts to your sub. You will have to 'manually' adjust the sub's high cut off to get the best integration of sub and mains as you can.