For a certain positive integer \(n\) less than 1000, the decimal equivalent of \(\dfrac{1}{n}\) is \(0.\overline{abcdef}\), a repeating decimal of period 6, and the decimal equivalent of \(\dfrac{1}{n+6}\) is \(0.\overline{wxyz}\) a repeating decimal of period 4. In which interval does \(n\) lie?

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