The sequence $a_n$ satisfies the equation $a_{m+n} + a_{m-n} = \frac{1}{2}(a_{2m} + a_{2n})$ for all $m \geq n \geq 0$. Given that $a_1 = 1$, find $a_{1995}$.

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