
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 that $m \in \mathbb{R}$, and there is a line $l: mx - (m^2 + 1)y = 4m$ and a circle $C: x^2 + y^2 - 8x + 4y + 16 = 0$.
(1) Find the range of possible slopes for the line $l$;
(2) Can line $l$ divide the circle $C$ into two arcs with a ratio of arc lengths of $\sqrt{3} : 1$? Why or why not?

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