The phrase "actually undertake" is correct and usable in written English.
It can be used when emphasizing the act of carrying out or committing to a task or responsibility.
Example: "Despite the challenges, we will actually undertake the project as planned."
Alternatives: "truly carry out" or "genuinely commit to".
Equally I noted that we continued to see others in the market posting rates at levels that were not representative of where they would actually undertake business.
Steps might include the deployment of civilian police and of teams of civilian experts to build judicial systems and, in some cases, to actually undertake civil administration.
With limited funding from the American government, the future of Mars and other missions are unclear — even though it will have the most advanced and powerful rockets and systems for sending people to space, Nasa might not be able to pay for it to actually undertake its journey.
Just because everyone expresses a readiness to A together doesn't mean that we all take the plunge and actually undertake it.
And it would probably be too ambitious for anyone to actually undertake.
Pass me another can of Monster energy drink!" action hero than Triple X. Consider: in the 80s, our action heroes were bulky muscle men, goliaths, so muscular they can't actually undertake some simple athletic movements, such as walking.
In other words, Congress actually undertook a useful investigation and made helpful recommendations.
I work a lot in actually undertaking land-use changes and approvals for projects.
It was not clear whether a significant review was actually undertaken in the eight months since the investigation was requested.
Those frustrated that Brand isn't actually undertaking an explicit revolutionary program are underestimating his political intelligence.
Opponents of the Mubarak government now say that senior officials in Cairo have adopted the vocabulary of reform without actually undertaking any.
