
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given an ellipse $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ and a parabola $y^{2}=2px(p > 0)$ share a focus $F_{2}$. The distance from a point $M$ on the parabola to the $y$-axis is equal to $|MF_{2}|-1$, and the intersection point $Q$ of the ellipse and the parabola satisfies $|QF_{2}|= \dfrac {5}{2}$.  
$(I)$ Find the equations of the parabola and the ellipse;  
$(II)$ A tangent line $y=kx+m$ to the parabola at point $P$ intersects the ellipse at points $A$ and $B$. Let the midpoint of line segment $AB$ be $C(x_{0},y_{0})$. Find the range of $x_{0}$.

Present the answer in LaTex format: \boxed{Your answer}
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