
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 $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ that passes through point $M( \dfrac {3}{2}, \sqrt {6})$ with a focal length of $2$. The left and right vertices of the ellipse are $A_{1}$ and $A_{2}$, respectively. $P_{1}$ is a moving point on the ellipse (not a vertex), and $P_{2}$ is the reflection of $P_{1}$ over the $x$-axis. The lines $A_{1}P_{1}$ and $A_{2}P_{2}$ intersect at point $E$.
(I) Find the standard equation of the ellipse.
(II) Find the trajectory equation of point $E$.

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