Let $D$, $E$, and $F$ be the feet of the altitudes from vertices $A$, $B$, and $C$ of an acute triangle $\triangle ABC$, respectively. Given that $AF = 28$, $FB = 35$, and $BD = 45$. Let $P$ be a point on segment $BE$ such that $AP = 42$. Determine the length of $CP$.

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