
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 circle $C: x^{2}+(y-1)^{2}=5$ and a line $l: mx-y+1-m=0$.

$(1)$ Determine the positional relationship between line $l$ and circle $C$, and explain the reason.

$(2)$ If line $l$ intersects circle $C$ at points $A$ and $B$, and $|AB|= \sqrt {17}$, find the value of $m$.

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