In a Rule, how can I prevent executing subsequent actions if the first action fails?
To provide conditional logic, you need the Rules Conditional module.

There's an open issue to document this further, and there's another meta issue which looks at integrating the conditional logic into the Rules module itself.


  This module provides Rules plugins for conditionally altering execution flow directly inside a group of actions. Provided plugins include:


Conditional
    If/(Else) If
    Else
Switch
    Case
    Default case
While