
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, $A(a,1)$, $B(4,b)$, $C(m,3)$, and $\sqrt{a-4}+\sqrt{b+2}=0$.  
$(1)$ Find the coordinates of $A$ and $B$;  
$(2)$ A line parallel to $AB$ passing through point $C$ intersects the $x$-axis at point $D$. If $S_{\triangle ABD}=6$, find the value of $m$.

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