If the neck relief is good, then you have a geometry problem. Normal neck relief is around .008". If you turn the truss rod, and the relief changes, then the truss rod is doing its work. If it doesn't change, then you have a truss rod problem. Remember to turn the truss rod 1/4 turn at a time, and with the strings slackened off. It can take a few minutes for the relief to change, so 1/4 turn, then wait, and check neck relief again. If the neck relief does not change, you probably have a broken truss rod, not common, but not unheard of either.
Assuming that the truss rod is OK, then you need to check the neck angle, according to what the previous posters wrote. Since you are the original owner, the bridge should not have been shaved, which is great. If the neck angle is off (straight edge hits the front of the bridge, or even the guitar top), then you need a neck reset. If it comes to the top of the bridge, or very slightly below (say, 1/32) you can delay the neck reset. I know opinions will vary, but I am adamantly opposed to shaving bridges; some are not and see it as a viable way of delaying a neck reset. If a bridge is shaved, and then the saddle is also shaved to reduce action, there will not be any way of restoring the guitar's original geometry, as well as increasing the possibility that the bridge will split. On the other hand, if you have a lot of saddle exposed, you can try to lower the saddle. Keep in mind that lowering the saddle has the effect of altering (actually, reducing) the string break angle, which affects the amount of downward pressure on the top, and can affect both tone and volume. This will vary in degree (tone) and amount (volume) depending on the guitar. If you need a neck reset, then do a neck reset, is my general approach.