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Cognitive radio (CR) techniques allow unlicensed secondary users (SUs) to opportunistically access underutilized primary channels that are licensed to primary users (PUs). We consider a multi-primary channel scenario in which the SUs cooperatively try to find these primary channel spectrum holes by limited spectrum sensing. The objective is to design the optimal sensing and accessing policy that maximizes the total secondary system throughput on the primary channels accrued over time, while satisfying a constraint on the probability of colliding with licensed transmissions. Although the problem can be formulated as a Partially Observable Markov Decision Process (POMDP), the optimal solutions are often intractable. As a result, we find the optimal myopic channel sensing policy that maximizes instantaneous total secondary system throughput on the primary channels at each time. The contributions of this paper include: 1) developing a universal optimal myopic channel sensing policy that is applicable for any number of primary channels, any number of SUs and any channel coefficients (assumed known); 2) formulation of a centralized spectrum sensing and decisionmaking architecture for cognitive secondary systems that allow exploitation of all available spectrum white spaces across the whole primary spectrum. We compare our combined sensing and accessing strategies with other proposed strategies and show that our proposed strategy outperforms them in terms of the resulting total secondary system throughput under the same constraints on collision with primary users.