The word 'forward' is correct and usable in written English. It can be used as a verb, an adverb, or an adjective. Example: He moved forward with his plan to build a new house.
You lost, stop being so damn jealous and move forward".
She has no compunction in moving Labour beyond our comfort zone and is determined to build a team ready to chart a route forward".
We need to pull together and move forward.
"So the real challenge for us as we debate our role in the EU is working out what we should be pushing forward, what we should be leading on within the EU, to make it – and us – a more effective economic and global power".
I'm already looking forward to getting the 2015-16 season underway".
He leaned forward.
"But I don't believe that to make a decision at this moment is the right way forward, either for Britain or for Europe as a whole.
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia