Casey values her own goals, but also appreciates her relationship and the goals of her partner. The type of conflict style Casey is most likely to use is

compromising

Explanation:

In this scenario, Casey is most likely to use a compromising conflict style. An individual using this style tends to be both assertive and cooperative since they are willing to trade some of their own needs in order to win concessions from the other party. Such as in this case Casey would pursue her own goals, but at the same time give up some of her pursuits in order to help in her partners goals, thus growing and nurturing the relationship.