'take up action' is correct and usable in written English.
You can use it to urge someone to take action, often in response to a situation or problem. For example: "It's time to take up action and demand change."
He predicted that the Palestinian government would take up action to ban Mr. Roed-Larsen.
Additional factors are the quick reflexes of different agencies to take up action at the aftermath of the vision creation, the local government was open to experiment with new and old arrangements and in this way, it reinvented its role without losing its governing responsibility.
It's time to give up hope and take up action.
The manifesto, Day explained, was meant to "inspire" others across the country "to take up action and do what these guys were doing, blowing up different Muslim targets".
Somebody who wasn't too serious but inspired millions to take up action against a world that was oppressing people and creating the kind of lacks that Mark Chapman felt so powerfully.
Is she willing to take up action with the Bahraini authorities in order to secure the release of Habib Ali Mubarak?
> Haggerty et al. (1994) propose another explanation for a marked decline in diarrhoea morbidity in the control group of their study of a hygiene intervention in DR Congo: the intense attention to diarrhoea that accompanied the trial raised awareness and stimulated villagers to take up actions that they knew were effective against diarrhoea a Hawthorne effect.
Or the Act only allows a woman to take up an action against her employer herself, without any great effect on other workers.
This year's agenda, though, favors the conservatives, as the court will take up affirmative action, voting rights, and abortion cases that appear likely to tip Anthony Kennedy, the swing vote, away from the liberals.
For one, expect to see the Supreme Court take up affirmative action again.
It is interesting that over 78% of the respondents did not take up any action eliminating or mitigating back pain.
