
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 point B(0, -2) and the ellipse M: $$\frac {x^{2}}{4}+ \frac {y^{2}}{2}=1$$. The line l: y = kx + 1 intersects the ellipse M at two distinct points P and Q.
(I) Find the eccentricity of the ellipse M.
(II) If $$k= \frac {1}{2}$$, find the area of △PBQ.
(III) Let point C be the other intersection of line PB with ellipse M. When C is the midpoint of PB, find the value of k.

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