"prompt action" is correct and usable in written English. You can use it when you want to emphasize that something should be done without delay. For example, "The situation requires prompt action to prevent further damage."
Hoover took prompt action.
Prompt action will be necessary.
Dad's involvement provoked prompt action.
Without prompt action, the economy will follow.
Without their prompt action, he would be dead.
Only public shame, it decided, would prompt action.
There are other reasons for prompt action, experts say.
My grateful thanks go to them for their prompt action.
Sex workers' safety and lives depend on prompt action.
In the meantime, other reforms need prompt action.
Archives|KERR SOON BACK IN FOLD.; Johnson Promises Prompt Action on Pitcher's Appeal.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com