What we should do is to try to improve the exam system.

1.what we should do整体作主语 译为“我们应该做的”
陈述句形式为we should do things,作主语时,将things提前并变为what以引导全句
相当于the thing that we should do
2.is做谓语,与主语构成主谓关系
3.to try作宾语
4.to improve the examsystem作宾语补足语,用以具体解释“尝试”去做的事