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After defeating the boss, collect the philosopher's stone that it drops, then go back home via the red door. Upon entering the door, the stone will melt and turn into a red liquid.

You can give it to Imouto with some milk bought from the vending machine. This will partially heal her ailment and allow her to stay up later. There are 2 different philosopher's stones you can get, one from the abyss boss, another from the bunny girl boss in the ruined forest, and you can treat Imouto's ailment a total of 2 times currently, with the 2nd treatment allowing her to stay up even later than the 1st.

Healing Imouto to allow her to stay up later is critical to unlocking the horror movie scene and adult video scene assuming you've already bought these items from the cat girl's van as these can only be watched late at night.

You can kill the abyss boss once per week or you can force it to respawn by using "The World" card.
After sister has taken two doses you can continue to use them on yourself for a power/max hp boost.