How do I reset my level of progress?

OP it is not possible to reset your soldier back to level 1 like the COD Prestige function. Your only option depending on your platform is to make a new account and link it to your existing Origin account. On PS3 this is free and if you link it to your Origin account and you're Premium your new soldier will also be Premium (except for validated premium stuff like the phantom bow). On Xbox 360 this requires a second Xbox Live Gold Subscription but on Xbox One it does not. For PC you will need to make a new Origin account and have to purchase BF4 again. 

There is a lot more to do in the game to extend your play - you can go for weapons mastery tags, there are a bunch of assignments from the expansion packs to do - and many more assignments if you become a premium member. If you've only been using a couple of classes you can expand your game by using classes that you normally don't which really changes the way your game experience is. I've actually got five soldiers since I play on all platforms and I play each one differently which had greatly extended my enjoyment of the game.