Let $a, b$ and $c$ positive real numbers such that $\dfrac{1}{a^2} +\dfrac{1}{b^2} +\dfrac{1}{c^2}=9$. If $M$ is the maximum value of the following expression
$\frac{1}{2a+b} +\frac{1}{2b+c} +\frac{1}{2c+a},$
enter $M^2$ as your answer.

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