As I became Francis' study partner I got closer to him, even though he hadn't trusted me. I could understand that, but I had my own goal too, and a plan to achieve that goal. The most important part of the plan is Francis' trust, so I had to gain his trust as soon as possible.
Something that is important for Francis to be able to be the heir to the throne is education. He must show his achievement in study, such as a good score for the annual evaluation. That way, he could gain support from powerful families more easily.
The Ashford family never let Francis catch people's attention. They assigned a tutor for him, who never taught him properly. That's why he used to sneak out from the palace and go to a bookstore to read something there. Unfortunately for him, since I became his study partner, he couldn't sneak out as usual.