wordplay - Six-words (------) Six-words (||||||)

Six-words:

My first is what a bouncer does if they think you're cool enough
My second is what my fourth does to your pain
My third is your surroundings on a grassy hill in summer
My fourth is taken to do my second to your pain
My fifth lives in places they do not own
My sixth is what you do with prize-winning animals

My first gathers liquid on to a surface
My second is where Leo kept going in Inception
My third is a branch of the US Military

My fourth is what you must do to solve this puzzle
My fifth is something shaped like a camper's home
My sixth is what well-off rude people may do to the less fortunate

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Inspired by Five-words and Four-words but this puzzle is a little different as there are two things being described. They're very tightly related but they're not twins.

Answer

ADMITS
DEADEN

SERENE
OPIATE
RENTER
BREEDS

What a fun little puzzle.