
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 a fixed point A(0, -4) and a moving point P on the circle x²+y²=4.

1. Find the trajectory equation of the midpoint C of AP.
2. If the line l passing through the fixed point $B(- \frac {1}{2}，-1)$ intersects the trajectory of C at points M and N, and $|MN|= \sqrt {3}$, find the equation of line l.

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