
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
If the equation $\frac{{x}^{2}}{9-k}+\frac{{y}^{2}}{k-1}=1$ represents an ellipse with its foci on the $y$-axis, then the range of values for the real number $k$ is         .

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