Here's what rhymes with logil.
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gear year clear near dear fear mere career beer rear deer peer shear sheer cheer pier queer mir feare leer veer vere vir yeare jeer sear sere appear sphere spear steer austere smear cashier revere sneer cohere servir amir emir tapir blear racketeer rainier leafier bawdier cushier runtier severe adhere premier unclear premiere reappear veneer auctioneer inhere vizir compeer besmear killdeer thornier brainier grainier hornier cafetiere cornier downier frontier pioneer sincere brigadier cavalier lithosphere domineer gazetteer profiteer triumvir balladeer marketeer lavalier junketeer atmosphere disappear engineer interfere volunteer persevere souvenir biosphere charioteer chevalier privateer troposphere yesteryear bombardier commandeer gondolier hydrosphere muleteer bandolier mutineer exosphere bandoleer bathysphere electioneer fusileer hemisphere financier insincere chandelier mountaineer stratosphere acyclovir pamphleteer mesosphere chanticleer scrutineer conventioneer