If it were mine....I look for simple stuff first ! I'm assuming the gun is clean..../ and you didn't do something foolish - like put it away wet for years...?? Remove the shells from the gun....
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a. Can you move the barrel selector / safety in all 4 directions..../ make sure its not on safe...( I know its stupid - but it happens ).../ then try to dry fire it.
b. Take the forend and the barrels off the gun.
Make sure there is nothing in the receiver - under cocking lever, etc ( like a pine needle - or debris ) that is preventing the gun from cocking.
Make sure the cocking lever and the cocking lever lifter are ok ../ lube them a little....
Put the gun back together...seat the forearm firmly. Make sure the barrels go back on the receiver smoothly and effortlessly...nothing binding.
As you open the gun - you should be able to hear the gun cock. See if you can dry fire. If one barrel fires...then shift safety on and off...and fire the 2nd barrel. Test it 2 or 3 times..
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If that didn't fix it ....I'd take the stock off...inspect firing pins, springs, etc..
for any issues...
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If any of that is beyond where you're comfortable ...then you need to find a knowledgeable gunsmith on Browning Citori's. Or talk to one of your buddies that can look at the gun personally and inspect it for you.
( this kind of diagnosis is hard to do over the internet - without the gun in our hands)....