This is the 326th most frequent Japanese word.
進め
"Proceed," "advance," or "go ahead."
進める is used as a transitive verb here, meaning 'to advance' or 'to carry forward' a process or activity.
プロジェクトを順調に進めるために計画を立てましょう。
Let's make a plan to proceed with the project smoothly.
進める indicates progressing or advancing an action—the verb is directed at the negotiation process.
交渉を早く進めるかどうかは相手次第だ。
Whether negotiations will progress quickly depends on the other party.
進めました illustrates a personal action of moving forward, showing experience or continuation.