Don’t use “convince” when you mean “persuade.” Convincing is for thoughts; persuading is for actions.

Incorrect: “I convinced the board to book Arnold Schwarzenegger as a speaker.”
Correct: “I persuaded the board to book Arnold Schwarzenegger as a speaker.”
Also correct: “I convinced the board that booking Arnold as a speaker would attract more people to the conference.”

Rule of thumb: If the word “to” is in the sentence, persuade yourself to use “persuade.” If there’s a “that,” convince yourself that “convince” is the right choice.