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Background
If you approach Rosemary in the fishing village (#2) while wearing the
Horrific Necktie, then an Inland Empire thought orb will appear over your head. If you click on it, then the necktie will get all excited about the blue bottle in Rosemary's hand, and it'll demand that you take a closer look.
When you talk to Rosemary, he'll mention that he's selling the
Blue Medicinal Spirit for 300 real. The necktie won't care how much it costs. It'll tell you that the bottle is necessary for "our END GAME," and it'll demand that you buy it. If you let Rosemary ramble on about the bottle for a while, then he'll mention that it's 98.7% alcohol and extremely flammable, and eventually he'll reduce its price to 3 real. This is when you should buy it.
Purchasing the
Blue Medicinal Spirit (whether you've been talking to the
Horrific Necktie or not) will trigger this task.
Walkthrough
You won't get any updates for this task until after meeting with Ruby during the task
Look for Ruby on the Coast. After completing that task, as you're making your way out of the
Feld Building (#1), if you're wearing the
Horrific Necktie, then you'll get another Inland Empire thought orb. When you click on it, the necktie will tell you that now is the time, and it'll demand that you put it into the
Blue Medicinal Spirit. If you comply, then you'll lose the necktie and the spirit, and you'll gain a
Spirit Bomb.
At this point in the game, all you'll be able to do is head to the
Whirling-in-Rags (#4) for the military tribunal. On your way there, when you reach the pawnshop (#3), you'll get another Inland Empire thought orb. If you click on it, then Inland Empire will warn you about the tribunal, and it'll recommend that you equip the
Spirit Bomb. Otherwise, if you're not on this quest, then you'll still get the thought orb, but Inland Empire will recommend that you equip your gun instead.
During the tribunal, you'll get a "challenging" Hand/Eye Coordination check to use the
Spirit Bomb. You can make this check easier by working your way through the other conversation options and passing the Rhetoric and Suggestion checks. If you pass the H/EC check, then you'll hit the mercenary leader with the
Spirit Bomb, and you'll get to say a touching farewell to your now Beautiful Necktie. Otherwise, if you fail the H/EC check, then your toss will miss everybody by a mile, and you'll lose a point of Morale (although you'll get it right back if you have 4 Volition). But either way, throwing the bomb will complete the task and earn you 30 xp.
1 - Feld Building
2 - Rosemary
3 - Pawnshop
4 - Whirling-in-Rags