Final answer:
Gracie used emotional manipulation, which influences behavior by affecting emotions, as opposed to logic, assertiveness, or collaboration.
Step-by-step explanation:
Gracie demonstrated the influence strategy of emotional manipulation by choosing to cry in response to being asked to eat her green beans. This strategy is an attempt to influence someone's behavior or decision by affecting their emotions, rather than using logic or collaboration. Assertiveness involves firmly stating one's own needs or demands, rational persuasion entails the use of logical arguments, and collaboration involves working together to find a mutually satisfying solution.