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Despite significant developments over the last decades, an analytical model which adequately describes plasma dynamics in the tokamak periphery region extending from the edge region to the far scrape-off layer is still missing. In this work, we present a new gyrokinetic model that retains the fundamental elements of the plasma dynamics at the tokamak periphery, namely electromagnetic fluctuations at all scales, the presence of strong flows, comparable amplitudes of background and fluctuating components, and a large range of collisionality regimes. Such model is derived within a gyrokinetic full-F approach, describing distribution functions arbitrarily far from equilibrium. For an efficient numerical implementation of the model, the gyrokinetic equation is projected onto a Hermite-Laguerre velocity-space polynomial basis, obtaining a gyrokinetic moment hierarchy. This extends a previously derived electrostatic drift-kinetic moment hierarchy [1] to an electromagnetic gyrokinetic regime. The treatment of arbitrary collision frequencies is performed by expressing the full-Coulomb collision operator in gyrocentre phase-space coordinates, and providing a closed formula for its gyroaverage in terms of the gyrokinetic moments, thereby filling a long-standing gap in the gyrokinetic literature. The use of systematic closures to truncate the moment-hierarchy equation, such as the semi-collisional closure, allows for an asymptotically correct recovery of both the fluid and the kinetic limits. In the electrostatic high collisionality regime, the novel hierarchy reduces to an improved set of drift-reduced Braginskii equations which have been widely used in scrape-off layer simulations. [1] R. Jorge, P. Ricci, and N. F. Loureiro. A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality. Journal of Plasma Physics, 83(6):905830606, 2017.