"continue to advance" is correct and usable in written English. You can use it to describe a person's progress or physical movement, among other things. For example, "She continued to advance in her career despite the challenges.".
The Houthis continue to advance.
We're going to continue to advance that".
The Bulls cannot afford to lose him if they want to continue to advance.
The Germans would instead continue to advance in the direction of the least enemy resistance.
"Let Europe's defense pole advance, and we will continue to advance toward NATO," he said.
I am proud to live in a state like California, where we can -- and must continue to -- advance women's health.
The world will [continue to advance technologically] only if the law can catch up," he said.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.