An Algebra problem by MSHT

Algebra Level 5

$\left\{\begin{matrix} x^2y-3x-1\geq mx\sqrt{y}(\sqrt{1-x}-1)^3 & & \\ \sqrt{8x^2-3xy+4y^2}+\sqrt{xy}=4y& & \end{matrix}\right.$ Let $$m$$ is an integer number satisfy the system of equality and inequality has a solution, and $$m\leq 12.$$

How many possible value of $$m$$ satisfy the conditional?

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