This is the 927th most frequent Japanese word.
進ん
"Progressing" or "advancing."
In this context, "進んでいる" is used to describe the progression or continuation of an activity, namely the project, conveying that it is moving forward as planned.
プロジェクトは順調に進んでいます。
The project is progressing smoothly.
Here, "進んだ" serves as an adjective-like form (past participle) to modify "方法" (methods), indicating these methods or techniques are advanced or developed.
彼は技術の進んだ方法を用いた。
He used advanced techniques.
In this sentence, "進んだ" illustrates a physical movement forward, indicating literal progression in space.