Publishing a Private version to a Public version through Data Action Advanced formulas

Hello Team,

I am working on SAC planning story where I would need to publish the data from a Private version to a Public version. I know there is a way to do this manually through an option "Version Management" with in the story. I would like to know if this is possible dynamically by clicking a button: data action trigger (through data action / advanced formula written in the data action) in the story.

I have looked for any function or formula to make this happen. However, I could not find it. Please advise me if you are aware of this solution / work around.