Multi-hypothesis testing, which is widely used in many application domains for discerning the true model governing the data, is often studied in a fixed sample-size setting. In such settings, the data-acquisition and decision-making processes are decoupled and the data collection policies are pre-specified. Motivated by the advantages of sequential sampling, this paper treats the inherently coupled problems of data-acquisition and decision-making for multi-hypothesis testing problems in the presence of multiple possible control actions. It aims to devise the quickest detection strategy by characterizing the minimum number of samples required to make a reliable decision as well as designing the dynamic attendant decision rules for selecting the best actions. This paper considers a setting in which the available control actions are co-dependent, which is a major distinction from the existing literature. Hence, the existing data-adaptive approaches lose their optimality guarantees for this problem as they fail to account for such dependence. This paper proposes a novel sampling strategy that incorporate the dependence of control actions into its decision rules. Performance analyses demonstrate the optimality properties of the proposed sequential approach under dependent actions and numerical evaluations highlight its gains over the existing ones.