For each real number \(x\), let \(f(x)\) be the minimum of the numbers \(4x+1\), \(x+2\), and \(-2x+4\). Find the maximum value of \(f(x)\). The original answer is in the form \(\frac{k}{m}\). Please provide the value of \(k + m\).

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