In a regular pentagon, we want to choose three vertices to form a triangle. How many such triangles can be formed? Additionally, if the probability that a randomly chosen set of three vertices forms a triangle is given by the fraction \(\frac{m}{n}\), where \(m\) and \(n\) are relatively prime positive integers, what is \(m+n\)? Let's think step by step and output the final answer within \boxed{}.
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