
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 that $F_1$ and $F_2$ are the left and right foci of the ellipse C: $$\frac {x^{2}}{3}+ \frac {y^{2}}{2}=1$$, respectively, and point P($x_0$, $y_0$) is on the ellipse C.
(1) Find the minimum value of $$\overrightarrow {PF_{1}}⋅ \overrightarrow {PF_{2}}$$;
(2) Given that line l: $y=k(x+1)$ intersects the ellipse C at two points A and B, and the line passing through point $$P(-1, \frac {2 \sqrt {3}}{3})$$ and parallel to line l intersects the ellipse C at another point Q, can the quadrilateral PABQ be a parallelogram? If so, find the equation of line l; if not, explain the reason.

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