
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
Let the function $f(x) = \frac{1}{\sqrt{(x^2+x+k)^2+2(x^2+x+k)-3}}$, where $k < -6$.  
Find the domain of $f(x)$ in interval notation;  
For $k < -6$, find the set of values for which $f(x) > f$ (expressed in interval notation).

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