
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 two parallel lines $l_1: x+y=0$ and $l_2: x+y+\sqrt{6}=0$ that intersect the line $m$ such that the segment of $m$ enclosed between $l_1$ and $l_2$ has a length of $2\sqrt{3}$, the possible inclination angles of $m$ could be among the following options:
1. $15^\circ$
2. $45^\circ$
3. $60^\circ$
4. $105^\circ$
5. $120^\circ$
6. $165^\circ$

Identify the correct sequence number(s) for the inclination angles of $m$. (List all correct sequence numbers.)

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