Are you making any progress in your work?
Tofugu always goes one step ahead, doesn't it?
Your daughter is advancing faster than the other students.
This word consists of kanji with hiragana attached. Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means advance so the verb vocab version means to advance.
Since this word consists of a kanji with hiragana attached, you can bet that it will use the kun'yomi reading. You didn't learn that reading with this kanji, so here's a mnemonic to help you:
In order to advance, you must sue Sue for her misdeeds against you. Imagine her standing in your way, literally. She keeps saying, "You'll have to sue me if you want to get past me!" So you do. You sue Sue.