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tumtitum You can kill the the long adder outright. You don't need it for this. You can use the mirror as an obstacle to push the Adder north. It sounds like you may have already gotten this part from your post, but I'll post details on how to do this in secret tags just in case.
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×Think about what will happen when Bethro is directly West of the mirror and the Adder is directly east. The Adder will move North to go around it (since it is visible to the brain). If you move North pushing the arrow along with you, you will have set up the exact same scenario for the next turn. You can keep doing this until the Adder is on the trapdoor.
It sounds as though your problem actually is that the adder doesn't want to keep going North after this. That's due to vertical/horizontal preference. You'll have to time things so that the Adder still favors vertical movement for at least one turn, but after that you can use the fact that the adder is brained to your advantage. Hint: mirrors AND force arrows are both brain visible obstacles.
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×Since the brain treats the arrows and mirror as obstacles, you can push the mirror on to the trapdoor after the adder and it will act unbrained since the brain can't pathmap to it. From there, just get into the same vertical column and you should be good.