Basically it means "advance, move forward" either physically or in an abstract way. For Number 1. you can also say, "We're advancing through the set of problems..." or solving the problems step by step. For Number 2., it means more like "I have to complete the auditor's report." (complete it step by step, almost like struggling with the report.)

Thanks, Kenan Custo, for clarifying the meaning of the idiom. That's the reason because I asked the question. I needed some clarification on the meaning.

To stay continuously engaged in a task, especially with meticulous attention or focus. Often used when the task is long-term or plodding. I think that your example sentences and my explanation comes from the same source. To simplify - to make progress in your work. Hope this helped :)