
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
$(1)$ Given two points $A(7,-4)$ and $B(-5,6)$, find the equation of the perpendicular bisector of the line segment $AB$. <br/>$(2)$ Find the equation of a line passing through the intersection of the two lines $2x+y-8=0$ and $x-2y+1=0$, and parallel to the line $4x-3y-7=0$.

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