
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 two points $A(-1,2)$ and $B(m,3)$, find:  
$(1)$ The slope $k$ of line $AB$;  
$(2)$ The equation of line $AB$;  
$(3)$ Given that the real number $m \in \left[- \frac{\sqrt{3}}{3} - 1, \sqrt{3} - 1\right]$, find the range of the inclination angle $\alpha$ of line $AB$.

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