
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 that the line $l$ passes through the point $(1, -2)$ and satisfies one of the following conditions:  
① Its slope is smaller than the slope of the line $y=x-1$ by $\frac{π}{12}$.  
② It is perpendicular to the line $y=-x+1$.  
③ Its $y$-intercept is $-1$.  

Supplement one of the above conditions in the following question and solve it.  
Question: Find the equation of the line $l$ passing through the point $(1, -2)$ and ____.

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