
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 line $l\_1$: $(a+1)x+3y+2=0$, and line $l\_2$: $x+2y+1=0$, find the value of $a$ such that $l\_1$ is parallel to $l\_2$ ($l\_1//l\_2$) and the value of $a$ such that $l\_1$ is perpendicular to $l\_2$ ($l\_1 ⊥ l\_2$).

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