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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