Mami the Psychic (1987)

Mami Sakura used to be a normal junior high school student, but she happened to acquire supernatural powers. Using her powers and with the help of her childhood friend, Kazuo Takahata, she solves mysterious occurrences.

She then saves people in trouble with her psychic powers, such as telekinesis and telepathy. When she senses someone needs help, she uses the "Teleportation Gun" (a heart-shaped brooch Takahata designs) and transports herself there. Mami's teleportation is only triggered when a projectile is flying toward her, and this locket that shoots out tiny marbles is a portable gadget for teleporting in a controlled way, rather than by chance. Her telekinesis can be precise to a cellular level, which enables her to transport cancerous cells out of one of her father's art critics. Her telepathy allows her to access people's thoughts and dreams.