First thing to do is locate the problem. Action is a product of three parts of the setup. First is set up the truss rod, 2nd is to adjust the action at the bridge, 3rd is to adjust the action at the nut. These things need to be done in that order.
Some time ago I put up a thread about setups to sort of collect what I thought was good info from the web. You can find it here, FWIW:
The truss rods come with little or no tension. It could be that when you strung it there was too much bow and it needs adjustment to take some of the bow out. It's the first thing to try if you have not adjusted it.
If that does not work, it may be that you need to lower the bridge...
I haven't heard about this problem with AG-1's but with some other set-neck guitars the angle is a bit too flat for the, and does not provide enough downward adjustment for the bridge. This is a trickier issue to solve, depending on how bad the problem is. You can recess the bridge post ferules to give your downward adjustment a couple of extra mm's. You could file down the slot in the saddles a bit. Hopefully one of these will do it. I am assuming that this is a set neck guitar...if so, yes, you can shim but you will have to unglue the neck (probably with heat and steam) to get it off so that you can shim it. If it is one of the bolt on SG type guitars, then it is much easier to shim...and you should probably do that rather than mess with the bridge.
If you have set the truss rod, and can get the (bridge) action right at the 17th fret using a capo on the first fret, then the problem has to be at the nut. You'll need to file the slots.
If none of that works...it could be that you have one or more high frets, and you may need to level them. Most kit necks require at least some leveling, particularly if you want the action very low.