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We prove non-perturbative Anderson localization and almost localization for afamily of quasi-periodic operators on the strip. As an application we establishAvila's almost reducibility conjecture for Schr\"odinger operators withtrigonometric potentials and all Diophantine frequencies, whose proof foranalytic potentials was announced in Avila's 2015 Acta paper. As part of ouranalysis, we derive a non-selfadjoint version of Haro and Puig's formulaconnecting Lyapunov exponents of the dual model to those of the originaloperator.

Non-perturbative localization on the strip and Avila's almost reducibility conjecture