
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
The slope of the line $\left(a+1\right)x+3y+3=0$ is $\frac{-a-1}{3}$ and the slope of the line $x+\left(a-1\right)y+1=0$ is $\frac{-1}{a-1}$. If the two lines are parallel, then the slopes are equal, so $-\frac{a-1}{3} = \frac{-1}{a-1}$.

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