continue by (doing something)
To persist in something or take the next step toward a particular goal or outcome. Once you're done cleaning the bathroom, you can continue by sweeping the hallway—that's the last area we need to clean before the dinner party.
continue by doing something
to keep going by starting to do something else or the next step. You are doing very well in this piano lesson. Please continue by playing the other sonata. After the interruption, Wally continued by explaining his position on the trade negotiations.