CBD says you take a 5+ save against any damage/crew loss suffered from an attack. AA says that you halve any damage that is inflicted by the attack. So by the wonderfull thing that is logic and semantics,
1. An attack strikes you, and you total up all the damage/crew that is inflicted in that attack.
2. AA takes place and halves that result.
3. Since you have now -suffered- that damage, you then take any CBD saves as appropriate.