Hello! To start the Latex Dungeon storyline, you simply need to spend some time in Hitomi's room. After a few times, you should see a [You Feel Watched] button, realizing that you are being watched. After pressing this button and experiencing the scene, you should see the [Run Towards The Door!] button as you continue to spend time in Hitomi's room. After this scene, you've started the Latex Dungeon storyline. When you go to sleep on a Monday, there will be a knock on the door and you will be taken there.
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You can also follow how to progress through all storylines, including the Latex Dungeon, from the blue [Guide] button on the left. It gets updated every step of the way and will tell you your next step.