
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 equation of circle ⊙C is $x^2+(y-1)^2=5$, and line $l$ passes through the point $(1,1)$.  
(1) If the slope angle of line $l$ is $\frac{\pi}{4}$, find the equation of line $l$;  
(2) Suppose line $l$ intersects circle ⊙C at points A and B, and if $|AB| = \sqrt{17}$, find the slope of line $l$.

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