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Algebra Level 5

\[\frac{b+c}{b^2+c^2+2(ab+bc+ac)}+\frac{a+c}{a^2+c^2+2(ab+bc+ac)}+\frac{a+b}{a^2+b^2+2(ab+bc+ac)}\]

Given that \(a,b\) and \(c\) are positive reals satisfying \(a^2b^2+b^2c^2+a^2c^2\leq666a^2b^2c^2\). Let \(P \) denote the maximum value of the expression above.

Find \( 10P\), round to the nearest integer.

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