Please reason step by step, and put your final answer within \boxed{}.
Let set $A = \{x \,|\, |x-a| < 1, x \in \mathbb{R}\}$, and $B = \{x \,|\, 1 < x < 5, x \in \mathbb{R}\}$. If $A \cap B = \emptyset$, then the range of the real number $a$ is ______.
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