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Each of these answers is the title of a Grateful Dead song with lyrics written by John Perry Barlow, but missing a single word:
  • looks LIKE RAIN
  • BLOW away
  • SALT LAKE city
  • estimated PROPHET
The added words are
  • looks
  • away
  • city
  • estimated
which together spell the answer LACE, as in "Crazy cat peekin' through a lace bandanna", in the (non-Barlow-authored) Dead song "China Cat Sunflower".