
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 C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$$ with a focal length of $$2 \sqrt {3}$$ and an eccentricity of $$\frac { \sqrt {2}}{2}$$, where its right focus is F. A line passing through point B(0, b) intersects the ellipse at another point A.  
(Ⅰ) If $$\overrightarrow {AB}\cdot \overrightarrow {BF}=-6$$, find the equation of the circumcircle of △ABF;  
(Ⅱ) If the line y=k(x-2) intersects the ellipse N: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}= \frac {1}{3}$$ at two points G and H, and $$| \overrightarrow {HG}|< \frac {2 \sqrt {5}}{3}$$, find the range of values for k.

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