Let \( P(x_1,y_1) \) and \( Q(x_2,y_2) \) be two distinct points on the ellipse \( \dfrac{x^2}{9} + \dfrac{y^2}{4} = 1 \) such that \( y_1 > 0 \) and \( y_2 > 0 \). Let \( C \) denote the circle \( x^2 + y^2 = 9 \), and \( M \) be the point \( (3, 0) \). Suppose the line \( x = x_1 \) intersects \( C \) at \( R \), and the line \( x = x_2 \) intersects \( C \) at \( S \), such that the \( y \)-coordinates of \( R \) and \( S \) are positive.
Let \( \angle ROM = \dfrac{\pi}{6} \) and \( \angle SOM = \dfrac{\pi}{3} \), where \( O \) denotes the origin \( (0, 0) \). Let \( |XY| \) denote the length of the line segment \( XY \).
Then which of the following statements is (are) TRUE?
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