
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 equation of the perpendicular bisector of the line segment $AB$, where points $A$ and $B$ are the intersections of the line $3x + 4y + 2 = 0$ and the circle ${x^2} + {y^2} + 4y = 0$.

A) $4x - 3y - 2 = 0$
B) $4x - 3y - 6 = 0$
C) $3x + 4y + 8 = 0$
D) $3x - 4y - 8 = 0$

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