As wrp96 says, you won't need to reclear security, but you will have a bit a hike from AA in T4 (or possibly even TBIT, though odds are much higher you will arrive T4). There are airside connections TBIT-T4 (just in case you arrive TBIT) and then a separate tunnel system T4-T5 and onward to T6. You can then connect between T6/7/8. This is not necessarily all straight forward to someone who does not know LAX, and it will certainly take some time to walk it, and this is the best case scenario assuming no delays on your ORD-LAX inbound. I would feel very uncomfortable with this tight connection.