
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 the equation of line $l$ is $3x + 4y - 12 = 0$, find the equation of line $l'$ such that:  
(1) $l'$ is parallel to $l$ and passes through the point $(-1, 3)$;  
(2) $l'$ is perpendicular to $l$ and the triangle formed by $l'$ and the coordinate axes has an area of 4.

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