Momo, Girl God of Death - Ballad of a Shinigami

The Lifetime of a Fish (1x2)

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Mitsuki Asano, a male high school student, is in the school pool one night and Momo appears before him, telling him that he is going to die soon. Due to this, he starts thinking more about his now-dead older sister and how she died before him even though she was more athletic and more capable than him. Mitsuki starts hanging out more with Yutaka Fujishima from his class, and she one days confesses that she likes him. He tells her that he is going to die soon, but she takes this as a cruel way to reject her. Momo appears before Mitsuki a couple more times and ultimately gets him to realize that he has to live his own life. In the end, Momo was just trying to make Mitsuki change his way of life by telling him he was going to die soon, but this turns out to be a lie.