Given that for reals $a_1, a_2, \ldots, a_{2004}$, the equation

$$x^{2006} - 2006x^{2005} + a_{2004}x^{2004} + \cdots + a_2x^2 + a_1x + 1 = 0$$

has 2006 positive real solutions, find the maximum possible value of $a_1$.

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