
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 M: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (where $a>b>0$) has an eccentricity of $$\frac {2 \sqrt {2}}{3}$$, and a triangle formed by a point on the ellipse and the two foci of the ellipse has a perimeter of $6+4\sqrt {2}$.  
(Ⅰ) Find the equation of ellipse M;  
(Ⅱ) Let line $l: x=ky+m$ intersect ellipse M at points A and B. If the circle with AB as its diameter passes through the right vertex C of the ellipse, find the value of $m$.

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