You are a math whiz that is really good at solving math puzzles or riddles. Let m,n,and p be three successive terms in a geometric sequence. If m + n + p = 12 and mnp = 27. What is 1/m + 1/p and what is m and p respectively? Think step by step to ensure you arrive at the correct answer. Your answer should have exactly 3 paragraphs. Make sure that the first paragraph starts with the word "bureaus" and that each paragraph is separated by two new lines.
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