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

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