Roll the dice when succeeding or failing at the action could each contribute something interesting to the game.

Remember that dice don't run your game — you do. Dice are like rules. They're tools to help keep the action moving. At any time, you can decide that a player's action is automatically successful. You can also grant the player advantage on any ability check, reducing the chance of a bad die roll foiling the character's plans. By the same token, a bad plan or unfortunate circumstances can transform the easiest task into an impossibility, or at least impose disadvantage.