The Aerial Combat phrase gives the CV/L a running start, especially if you arm her with your best anti-ship planes, and if the flagship CV/L can end the fight by her second shelling turn, then all's usually good and well =3. I would also equip a 15.5cm Triple Gun or, even better, the Aircraft Maintenance Personal on her so that she could attack and hopefully finish off the last enemy before the FBB could get her chance. The key is to deny the FBB or in fact any of the battleships the chance to fight
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That said, I guess using FBBs is not recommendable for CAs since they lack the CV/Ls' starting advantage and is not likely to outgun them as well