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We initiate the study of algorithms for constraint satisfaction problems with ML oracle advice. We introduce two models of advice and then design approximation algorithms for Max Cut, Max 2-Lin, and Max 3-Lin in these models. In particular, we show the following. • For Max-Cut and Max 2-Lin, we design an algorithm that yields near-optimal solutions when the average degree is larger than a threshold degree, which only depends on the amount of advice and is independent of the instance size. We also give an algorithm for nearly satisfiable Max 3-Lin instances with quantitatively similar guarantees. • Further, we provide impossibility results for algorithms in these models. In particular, under standard complexity assumptions, we show that Max 3-Lin is still 1/2+η hard to approximate given access to advice, when there are no assumptions on the instance degree distribution. Additionally, we also show that Max 4-Lin is 1/2 + η hard to approximate even when the average degree of the instance is linear in the number of variables.