進み is read as すすみ (susumi) and means progress.
すすみ
susumi
しんしゅつ
advance (to the next round of a competition)
しんがく
advancing to the next stage of education
しんこう
progression (e.g. chord progression)
しんたい
remaining in one's post or resigning
しんろ
one's future course (e.g. after graduating high school)
しんか
evolution
しんぽ
progress
しんにゅう
entry
すすむ
to do of one's own free will
すすめる
to advance
しんかろん
evolutionary theory
しんげん
advice (to a superior)