
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 $l_{1}$ is $3x+4y-12=0$.

$(1)$ If line $l_{2}$ is parallel to $l_{1}$ and passes through the point $(-1,3)$, find the equation of line $l_{2}$.

$(2)$ If line $l_{2}$ is perpendicular to $l_{1}$ and the area of the triangle formed by $l_{2}$ and the two coordinate axes is $4$, find the equation of line $l_{2}$.

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