The phrase "and then engaged" is correct and usable in written English.
It can be used to describe a sequence of actions where someone becomes involved or committed to something after a prior event.
Example: "After discussing the project details, the team members agreed on the plan and then engaged in a brainstorming session."
Alternatives: "and subsequently participated" or "and then took part".
Chain graduated in chemistry and physiology from the Friedrich Wilhelm University of Berlin and then engaged in research at the Institute of Pathology, Charité Hospital, Berlin (1930 33).
The two separated shortly afterward, in January 1995, and then engaged in an expensive divorce battle that ended in her placing business ownership over cash.
There he donned a Tatar hat, stuck his face in a vat of yogurt to bob for coins and then engaged a Tatar girl in arm wrestling.
He received his M.D. degree in 1883 from the University of Michigan, Ann Arbor, and then engaged at Rochester in the private practice of medicine and surgery with his father and later with his younger brother Charles Horace Mayo.
The Jets traded up to select Revis with the 14th pick in 2007 and then engaged in contentious negotiations with his representatives that spurred a 20-day holdout that summer.
"Autumn Serenade" was just about flawless, but on "They Say It's Wonderful" Mr. James misjudged his re-entry after a double-time solo by Mr. Tyner, and then engaged in some aerial maneuvers that felt ill-considered and glib.
He pulls your knickers off, performs cunnilingus on you and then engages you in penetrative sex.
Frequently, they start with small crimes and then engage in ever bigger misdemeanours to conceal their wrongdoing.
We want to make it easy to join and then engage our members over time with effective communication and storytelling.
Biggest bore: Audiences texting, tweeting and eating during a show, and then engaging in a ritual standing ovation.
She carefully grooms her target, a student named Jack, and then engages him in a queasy, compulsive affair.
