Since this word has okurigana (hiragana attached to the kanji) you know that it's probably going to be the kun'yomi reading, which you didn't learn with the kanji. Here's a mnemonic to help:
You are moving your lawsuit forward against Sue. But now she says that YOU'RE the problem. "Sue, sue me," (すすめ) you say as you continue to advance the lawsuit. Make sure to say "me" like "mehh," in a really snobbish way.
Thank you for giving us advice on advancing our research.
With this snow, we can't move the construction forward anymore.
Please move your work forward at the current pace.