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We propose a simple modification of a well-known Random Walk algorithm for solving the Satisfiability problem and analyze its performance on random CNFs with a planted solution. We rigorously prove that the new algorithm solves the Full CNF with high probability, and for random CNFs with a planted solution of high density finds an assignment that differs from the planted in only e-fraction of variables. In the experiments the algorithm solves random CNFs with a planted solution of any density.