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Join Starfleet. Fast reaction time not required!
(media.giphy.com)
sometime i think the pace of DS9 is tooooo slow, but maybe its the valium
At least aiming their phasers while they were unsure would have given them a chance to react once the changeling transformed.
I mean, rule #1 of firearm safety is not to point the loud end at something you don't want to kill, certainly not a colleague... not sure what they teach on day one of Phaser School but I suspect it's not too far off!
Certainly not the fucking medic.
I bet the first thing they teach you is to set the phasers to stun
Of course, but when you don't know who is a deadly foe, there's a bit more subtlety than having to be defenseless because you aren't certain. The risks can never be reduced to zero, and the safety of you and your team can't be ignored.