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Assuming I interpreted ur comment right, I think the reason why she didn't avoid Ryu in this life is exactly because she's not particularly obsessed with him as she's come to realize how loved she actually is by her father, it's the same way she's not being a brat toward people anymore unlike the first life.
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if im not mistaken she realised that she had a past life around the end of her second life. and i think it was mentioned she was cold to ML in her second life because of what people might say if she tries to get close. especially when (she thinks) he was only nice to her just because she was his masters daughter
In her first life, I mean the life when she was killed by Yayul, she already remembered the novel, right? Because in the novel that she remembered, her character was supposed to be obsessed with Ryu(ML) but she deliberately avoided him. But despite knowing the novel, she didn't do anything else to change it? I'm kinda confused.