Simply put, just give your AAdvantage number to Cathay so that your flight on CX is creditted properly into your AAdvantage account. Then just show up at the airport and all your elite privileges that you're used as AA Plat will be reciprocally accepted by Cathay as their system automatically knows that AA Plat = OW Sapphire level; priority business class check-in (even when flying in economy), CX lounge access, priority boarding, etc.