
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
In the Cartesian coordinate system $xOy$, given points $A(-3, -4)$ and $B(6, 3)$, and the line $l: x + my + 1 = 0$.

(1) Find the equation of the perpendicular bisector of $AB$;  
(2) If the distances from points $A$ and $B$ to line $l$ are equal, find the value of $m$.

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