\[x^6+5x^5y+10x^4y^2+kx^3y^3+10x^2y^4+5xy^5+y^6\ge 0\]
Find the absolute value of the smallest possible \(k\) such that the inequality above is true for all non-negative reals \(x\) and \( y \).
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Note:You may use the algebraic identities below.