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)
しんだい
remaining in one's post or resigning
しんか
evolution
しんぽ
progress
しんにゅう
entry
しんろ
one's future course (e.g. after graduating high school)
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)