Find the minimum

Algebra Level 4

\[\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\le\frac{a+b+c}{2}\]

Let \(a,b,c >0\) satisfying the inequality above.

Find the minimum value of the expression below. \[P=2(a^3+b^3+c^3)+4(ab+bc+ca)+abc \]

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