Path planning for autonomous search and tracking of multiple objects is a critical problem in applications such as reconnaissance, surveillance, and data gathering. Due to the inherent competing objectives of searching for new objects while maintaining tracks for found objects, most current approaches rely on multi-objective planning methods, leaving it up to the user to tune parameters to balance between the two objectives, usually based on heuristics or trial and error. In this paper, we introduce UniSaT (Unified Search and Track), a novel unified-objective formulation for the search and track problem based on Random Finite Sets (RFS). Our approach models unknown and known objects using a combined generalized labeled multi-Bernoulli (GLMB) filter. For unseen objects, UniSaT leverages both cardinality and spatial prior distributions, allowing it to operate without prior knowledge of the exact number of objects in the search space. The planner maximizes the mutual information of this unified belief model, creating balanced search and tracking behaviors. We demonstrate our work in a simulated environment, presenting both qualitative results and quantitative improvements over a multi-objective method.