A triangle has side lengths \(a\), \(b\), and \(c\) such that \(a \leq b \leq c\) and all side lengths are integers. Given that \(b + c > a\), \(a + c > b\), and \(a + b > c\), what is the smallest possible perimeter of a triangle with a side length of 7 and another side length of 10? Let's think step by step and output the final answer within \boxed{}.
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