
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 ellipse $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (where $a>b>0$) passes through point M ($$\frac {3}{2}, \sqrt {6}$$), and its focal length is 2. The left and right vertices are A<sub>1</sub> and A<sub>2</sub>, respectively. P<sub>1</sub> is a moving point on the ellipse (not a vertex), and point P<sub>2</sub> is the symmetric point of P<sub>1</sub> with respect to the x-axis. The line A<sub>1</sub>P<sub>1</sub> intersects with A<sub>2</sub>P<sub>2</sub> 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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