
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 line $l$: $mx - (m^2 + 1)y = 4m (m \geqslant 0)$ and the circle $C$: $x^2 + y^2 - 8x + 4y + 16 = 0$, there are several conclusions:

1. The slope angle of line $l$ is not obtuse;
2. Line $l$ must pass through the first, third, and fourth quadrants;
3. Line $l$ can divide circle $C$ into two arc segments with a ratio of $\frac{1}{2}$;
4. The maximum chord length of the intersection of line $l$ and circle $C$ is $\frac{4\sqrt{5}}{5}$;

Write out the numbers of all correct statements.

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