In \(\triangle ABC\), point \(D\) is on \(AC\) and point \(F\) is on \(BC\). It is given that \(AB \perp AC\), \(AF \perp BC\), and \(BD = DC = FC = 1\). Find the length of \(AC\). The original answer is in \(\sqrt[k]{m}\) format, please give the value of k + m.

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