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I think it necessary to have a break, because then she can think more if she wanted to be with him. She was getting used to the feeling of being “lonely” and that’s not good. So I think that the break helped her to thing and get a hold of her own feelings. And she was crying because she didn’t want to actually break up with sempai.
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It's typically called a "cool off". You're basically together but sorting things out and getting time alone. She was having a hard time understand if she still has feelings for him the same way like last time. She also feels guilty for feeling mad about him. She basically thought he doesn't love her anymore and feels bad for feeling that way. It's why her resolve after the cool off was that she has learned to see how much he loves her based on his subtle gestures and the way he talks and texts.
Wait I’m so confused with why they took a break. I understand why he wanted to take a break cause he want to focus more on his admission to college and he didn’t want to jeopardize both his relationship and his future, but I don’t understand her. Was it cause she was like second guessing their relationship and wasn’t sure it would last or not? I’m not hating on her I just don’t understand her thoughts during the break and why she was crying and such.