Innate Inequality

Algebra Level 3

Let \(a_1,a_2,a_3,\ldots,a_{173}\) be positive real numbers such that \(a_1+a_2+a_3+\ldots+a_{173}=174\). Find the minimum possible value of

\[\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+\frac{a_3^2}{a_3+a_4}+\ldots+\frac{{a_{173}}^{2}}{a_{173}+a_1}.\]

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