"decisively engage" is a correct and usable phrase in written English.
You can use it in the context of making a strong commitment to something. For example, "My team will decisively engage in this project to ensure the best possible results."
Not all of the reactions were positive: several of Duncan's captains were criticised for their failure to rapidly and decisively engage the enemy, including Captain Wells of Lancaster.
The failure of the Axis forces to decisively engage the Partisans during these operations necessitated a further major offensive, Operation Trio, in the area immediately south of where Operations Southeast Croatia and Ozren had taken place.
In 1947 in Mumbai, Syed Haider Raza and Francis Newton Souza (1924-2002) helped start the Progressive Artists Groupp, which decisively engaged with European modernism of the day.
Although the Viet Cong managed to avoid becoming decisively engaged, around 90 were killed and five captured, as the Australians maintained their blocking positions.
Regardless, this restriction had only served to make B Company's task all the more difficult, with Mackay facing demands to complete the action while at the same time not become decisively engaged and unable to withdraw his company.
Marlborough – with renewed self-assurance – moved decisively to engage them.
From this location, the Japanese naval forces hoped to engage and decisively defeat any Allied (primarily U.S). naval forces, especially carrier forces, that responded to Hyakutake's ground offensive.
"This has left us ill prepared to engage early, proactively, and decisively to prevent threats from evolving into large scale civilian atrocities".
How readily and open-mindedly people will engage scientific information depends very decisively on context.
The preferred policy option, in addition to the travel ban, would be to engage African governments and to strengthen their capacity to deal decisively with these terrorist groups.
Certain performers sing all their notes in high C. It's never wholly clear what makes the difference between a Frank Sinatra and Joan Sutherland and any number of completely capable and fully engaged but decisively not comparable other performers of the same music.
