
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 P(1, 1), a moving line $l$ passes through point P and intersects circle $C: x^2+y^2-2y-4=0$ at points A and B.  
(1) If $|AB| = \sqrt{17}$, find the slope angle of line $l$;  
(2) Find the equation of the trajectory of the midpoint M of segment AB.

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