Let \(z\) and \(w\) be complex numbers such that \(|z + 4 + 3i| = 5\), \(|w - 1 - 2i| = 3\), and \(|z + w| \leq 7\). What is the maximum possible value of \(|z - w|\)? Let's think step by step and output the final answer within \boxed{}.
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