I am writing a grant application as a sole PI, and it is not clear to me whether I should use singular or plural terms. As an example, currently I have a sentence like this:
"Based on previous work, I got to the conclusion that the present approach X to problem Y is inappropriate. Therefore, in paper Z we developed an alternative approach which I plan to pursue further in the proposed research.
The reason for the switches between "I" and "we" is that the conclusion is mine, but paper Z is a paper I wrote with a coauthor, and the plan to pursue this further is again mine alone. While the terms reflect the reality, it seems bad English to switch back and forth between singular and plural.
In usual research papers, I often use "we" even when I am a sole coauthor, since this is convenient and quite common in my field (computer science). However, using "we" in a personal grant application seems inappropriate.
What is a better style for writing sentences such as the above?