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Caching at mobile devices and leveraging cooperative device-to-device (D2D) communications are two promising approaches to support massive content delivery over wireless networks while mitigating the effects of interference. To show the impact of cooperative communication on the performance of cache-enabled D2D networks, the notion of device clustering must be factored in to convey a realistic description of the network performance. In this regard, this paper develops a novel mathematical model, based on stochastic geometry and an optimization framework for cache-assisted coordinated multi-point (CoMP) transmissions with clustered devices. Devices are spatially distributed into disjoint clusters and are assumed to have a surplus memory to cache files from a known library, following a random probabilistic caching scheme. Desired contents that are not self-cached can be obtained via D2D CoMP transmissions from neighboring devices or, as a last resort, from the network. For this model, we analytically characterize the offloading gain and rate coverage probability as functions of the system parameters. An optimal caching strategy is then defined as the content placement scheme that maximizes the offloading gain. For a tractable optimization framework, we pursue two separate approaches to obtain a lower bound and a provably accurate approximation of the offloading gain, which allows us to obtain optimized caching strategies.