
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: $$\frac {x^{2}}{2}+y^{2}=1$$, point A (1, $$\frac {1}{2}$$), and point B (1, 2).
(I) If line l intersects ellipse C at points M and N, and A is the midpoint of segment MN, find the slope of line MN.
(II) If line l<sub>2</sub>: y = 2x + t (t ≠ 0) intersects ellipse C at points P and Q, find the maximum area of △BPQ.

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