The phrase "act nonetheless" is correct and usable in written English.
It can be used to indicate that someone will proceed with an action despite any obstacles or contrary circumstances.
Example: "Despite the challenges we faced, we decided to act nonetheless and move forward with the project."
Alternatives: "proceed anyway" or "take action regardless".
Attacked as extravagant, the Judiciary Act was nonetheless passed, and O'Connor resigned his portfolio on 24 September, resigning from the Senate on 27 September.
Even though physicians as humans are not perfect, and thus cannot act virtuously, nonetheless they can make appropriate decisions, take appropriate actions, and "do the right thing".
Ineptly made, atrociously acted, it nonetheless had a bovine cheeriness about it that made it very hard to dislike.
"Even if no direct encouragement or directive is given," the report said, "many children raised with holistic thinking may nonetheless act according to the group's 'unspoken' rules".
So now there is a private member's bill which, alas, does not have the force of a US Senate's draft act, but which nonetheless signals parliamentary concern over FCO foot-dragging.
While they are too needy, greedy and confused to be allegorical figures, the rich man, his wife and the stranger nonetheless act out a grim little fable of social relations in modern Germany.
Though not the Dark Power itself, bags in trees nonetheless act as its minions; or, to put it another way, nothing makes a neighborhood look scarier than bare-branch trees draped with plastic-bag shreds above a razor-wire fence similarly fluttering and bestrewn.
Even if, as in China, the public voice is muted, both elite and international opinion nonetheless act to request, if not require, policies that regulate the science in the public interest - not only in terms of risk and safety but also the sensitivities of cultural values.
The leaders of several other rich-world central banks have also acted boldly.Nonetheless, Mr Bernanke's academic research gave him an acute appreciation of the risks posed by dysfunctional financial markets.
