DVM is right. I would try a shim. Truss rod is not really for action. You want to first ensure proper relief them adjust saddle height to your preference keeping in mind the height for each along the radius. If you are not able to set it reasonably low without buzzing you can then try a shim to give a bit of lift to help you in this regard. If this doesn't help you more than likely will need a fret leveling as a fret or frets are not their proper height and hitting the strings.

Also the comment about strays inherently having higher action is nonsense - I have the action incredibly low on my JV and there isn't any buzzing and plays as fast as my Charvel's neck. Learning how to adjust your guitar(s) is a great skill to learn. No one knows how you like your guitar to play like you do.