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If $a \in \mathbb{R}$ and the equation

$-3\big(x-\lfloor x \rfloor\big)^2+2\big(x-\lfloor x \rfloor\big)+a^2=0$

has no integral solution, then all possible values of $a$ lie in the interval $\text{\_\_\_\_\_\_\_\_\_\_}.$

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