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Let $$\alpha, \beta$$ be the distinct roots of the equation $$x^2 - (t^2 - 5t + 6)x + 1 = 0, t \in \mathbb{R}$$ and $$a_n = \alpha^n + \beta^n$$. Then the minimum value of $$\frac{a_{2023} + a_{2025}}{a_{2024}}$$ is
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