I am currently learning about NP and coNP related content and have been exposed to the$NP \overset{\text{?}}{=}coNP$ problem.
I would like to know what are the directions to work on if I want to prove that $NP=coNP$? For example, currently I know that if I can prove that a coNP-complete language belongs to NP, then I can prove that $NP=coNP$.
If I want to prove that $NP \neq coNP$, what are the directions to work in, or what results have already been obtained?