The first thing you should do to start cleaning a rifle is to pass a couple of solvent soaked patches down the bore.
Then,use or insert a q-tip about an inch down the muzzle and see if you have any carbon off of the lands(thick black lines).If you do stop wasting patches and use a solvent soaked brush to get it all out(takes just one pass through the bore).
Insert the q-tip again and see if it is gone and if it is, see if there is any copper and if there is, deal with that.
Avoid using JB with that streak of carbon still in the bore.You don not want to get that carbon on a patch and then stroke it down the bore.

You also REALLY need to go hunting.