
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
If the length of the segment cut off by two parallel lines $l_1: x-y+1=0$ and $l_2: x-y+3=0$ on line $m$ is $2\sqrt{2}$, then the possible slopes of line $m$ are:  
① $2-\sqrt{3}$;  ② $\frac{\sqrt{3}}{3}$;  ③ 1;  ④ $\sqrt{3}$;  ⑤ $2+\sqrt{3}$  
The correct answer number(s) is/are ______.

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