
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 a line $l:x-my+\sqrt{3}m=0$ has a point $M$ on it that satisfies the product of the slopes of the lines connecting $M$ to points $A(-1,0)$ and $B(1,0)$, denoted as $k_{MA}$ and $k_{MB}$, is $3$, then determine the range of the real number $m$.

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