
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 equation of the ellipse $C$ is $\dfrac{x^{2}}{9-k}+ \dfrac{y^{2}}{k-1}=1$.
$(1)$ Find the range of values for $k$;
$(2)$ If the eccentricity of the ellipse $C$ is $e= \sqrt{\dfrac{6}{7}}$, find the value of $k$.

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