
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
Find the equations of the line $l$ that satisfy the following conditions:  
$(1)$ Suppose line $l$ passes through point $P(-1,-3)$ and its angle of inclination is twice that of the line $y=3x$;  
$(2)$ Suppose line $l$ passes through point $A(-1,1)$ and the distance from point $B(2,-1)$ to line $l$ is maximized.

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