
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 circles $F_{1}\;:\;(x+2)^{2}+{y}^{2}=4$ and $F_{2}\;:\;(x-2)^{2}+{y}^{2}=36$. If the moving circle $M$ is externally tangent to circle $F_{1}$ and internally tangent to circle $F_{2}$, find:<br/>$(1)$ The equation of the locus $C$ of the center $M$;<br/>$(2)$ The equation of the line $l$ intersecting the locus $C$ from $(1)$ at points $A$ and $B$, where $Q(2,-1)$ is the midpoint of segment $AB$.

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