What is the origin of the idiom "carrot and stick" and when to use it?

The idiom "carrot and stick" refers to a strategy that combines both rewards (the "carrot") and punishment (the "stick") to motivate or influence someone's behavior. The origin of this expression can be traced to the imagery of motivating a donkey to move by dangling a carrot in front of it while also threatening to strike it with a stick if it doesn't comply. This approach has been used historically to guide or incentivize individuals, often in situations where they may be resistant or reluctant.