Let \(S\) be the set of permutations of the sequence \(1,2,3,4,5\) for which the first term is not \(1\). A permutation is chosen randomly from \(S\). The probability that the second term is \(2\), in lowest terms, is \(\frac{a}{b}\). Please find the value of \(a + b\).

Let's think step by step and output the final answer within \boxed{}.
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