
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 lines $l_1: ax+2y+6=0$ and $l_2: x+(a-1)y+a^2-1=0$. When $a$ \_\_\_\_\_\_, $l_1$ intersects $l_2$; when $a$ \_\_\_\_\_\_, $l_1$ is perpendicular to $l_2$; when $a$ \_\_\_\_\_\_, $l_1$ coincides with $l_2$; when $a$ \_\_\_\_\_\_, $l_1$ is parallel to $l_2$.

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