I apologize if it has been asked a thousand times. Googling the loom just brings up dozens of old articles on how to open it.
I'm pretty sure I finished the quest line when it came out, I have done Ada-1's bounties, I have rigid synthcord by the hundreds in my mailbox. The quest isn't on her or in my log, and I still can't use the Loom.
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Check abandoned quest kiosk.