proceed is very much just continue, go on, carry on. Like for example, if you were discussing about the feasibility of a certain plan, the conclusion could very well be: "I guess we can proceed as planned", meaning we can carry on with our plans as we have intended to. you could even use it to tell someone to start doing something through saying, "please proceed with the project now" do let me know if I could be of further help :)

Thanks, bro.

Keep searching, you will find a way to use it. = Proceed with your searching, you will find a way to use it.