
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 the hyperbola $C: x^2-\frac{y^2}{3}=1$ and the line $l: y=kx+m(k≠±\sqrt{3})$ have a unique common point.<br/>$(1)$ Point $Q(2,3)$ lies on the line $l$, find the equation of the line $l$;<br/>$(2)$ Let $F_{1}$ and $F_{2}$ be the left and right foci of the hyperbola $C$, $E$ be the right vertex, and the line passing through point $F_{2}$ and intersecting the right branch of the hyperbola $C$ at points $A$ and $B$ (where point $A$ is in the first quadrant). Let $M$ and $N$ be the incenter of triangles $\triangle AF_{1}F_{2}$ and $\triangle BF_{1}F_{2}$, respectively.<br/>① Is the abscissa of point $M$ a constant value? If yes, find the value of the abscissa; if not, explain why;<br/>② Find the range of values for $k_{MF_2}+k_{NF_2}$.

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