
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 straight line $l$ passes through point $P$ and intersects with 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 trajectory equation of the midpoint $M$ of line segment $AB$.

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