\[ \begin{cases} x+y \leq 1 \\ \dfrac2{xy} + \dfrac1{x^2+y^2} = 10 \end{cases} \]

Find \(x\) and \(y\) such that they satisfy the constraints above. Submit your answer as \(|x+y|\).

If you think there are no \(x\) and \(y\) satisfying these equations, enter 123456 as your answer.

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