
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 $xOy$, points $A(-3,-4)$ and $B(6,3)$ are given, and the line $l$: $x + my + 1 = 0$.
(1) Find the general equation of the perpendicular bisector of segment $AB$;
(2) If the distances from point $A$ to point $B$ to line $l$ are equal, find the value of $m$.

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