
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 the parabola $y^{2}=4mx(m > 0)$ whose directrix intersects the $x$-axis at $F_{1}$, and an ellipse with foci $F_{1}$, $F_{2}$ and eccentricity $e= \frac {1}{2}$ intersects the parabola at point $E\left( \frac {2}{3}, \frac {2 \sqrt {6}}{3}\right)$. A line drawn from $F_{1}$ intersects the parabola at two distinct points $P$ and $Q$, and it is given that $\overline {F_{1}P}=\lambda \overrightarrow{F_{1}Q}$.  
(I) Find the equations of the parabola and the ellipse;  
(II) If $\lambda\in\left[ \frac {1}{2},1\right)$, find the range of $|PQ|$.

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