
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 C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ has an eccentricity of $$\frac {1}{2}$$, and the point $$( \sqrt {3}，- \frac { \sqrt {3}}{2})$$ is on the ellipse C.  
(Ⅰ) Find the equation of ellipse C;  
(Ⅱ) A line l through the right focus F of ellipse C intersects the ellipse at two distinct points M($x_1$,$y_1$) and N($x_2$,$y_2$). If point P is symmetric to point N with respect to the x-axis, determine whether line PM always passes through a fixed point. If so, find the coordinates of that point; if not, explain why.

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