Where is the Cave entrance?

When you become Green, the Fellowship and the Illuminati factions will arrive at your room to ask which faction will you join.

If you choose Fellowship, you will end up in a mission to find the Grindstone.

Per the description of the mission, you have to find the cave entrance.

Where is the entrance of the cave? I already searched everything past PAL and everything... still can't find it.

I just found it way past PAL room, thru the door to the next map.

Here is a picture of the location:

Go to the next map where PAL is, continue thru the scaffolding and check the room named Reactor Officer Office. The green arrows point to the room where the cave entrance is.

Ignore the blue arrow room because those exclamation marks seems to be a bug since you can't interact with them.