
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 points $A(-1,3)$, $B(5,-7)$ and line $l$: $3x+4y-20=0$.  
$(1)$ Find the equation of the line $l_{1}$ that passes through point $A$ and is parallel to line $l$.  
$(2)$ Find the equation of the line $l_{2}$ that passes through the midpoint of $A,B$ and is perpendicular to line $l$.

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