
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: $$\frac {x^{2}}{4}+y^{2}=1,$$  
(1) If a line $l$ passes through point Q $(1, \frac {1}{2})$ and intersects the ellipse C at points A and B, find the equation of line $l$ such that Q is the midpoint of AB;  
(2) Given a fixed point M $(0, 2)$, and P is any point on the ellipse C, find the maximum value of the segment PM.

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