Risky Plan.
Though he thought about the quest a lot during the time he was in his classroom and during the time he was heading home, he still thought about it again when he arrived home.
As said, he kept making strategies upon strategies. The major thing he was strategizing about was how to know the things he wanted to know about Miss Amaya.
Of course, he'd simply have to check out her status to know the things he wanted to know about her...
But how would he go about checking out her status? How would he get close to her to check out her status?
Of course, he can't just stay anywhere and check out her status, he'd have to be a few meters away from her to do so. Or he can be super close to her to do so.
He kept on strategizing on how to go about this, and was he able to come up with a nice strategy? Yes. He'd implement it at the right time once he reaches school.