
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 $C: (x+1)^2 + (y-1)^2 = 8$ and a line $l: mx-y+2-m=0$.  
$(1)$ For $m \in \mathbb{R}$, can the line $l$ be tangent to the circle $C$? If tangent, find the equation of the tangent line. If not tangent, explain the reason.  
$(2)$ Let the line $l$ intersect the circle $C$ at points $A$ and $B$. If $\triangle ABC$ is an isosceles right triangle, find the equation of line $l$.

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