
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 \( k \) be a real number, and define \( f(x)=\frac{x^{4}+k x^{2}+1}{x^{4}+x^{2}+1} \). If for any three real numbers \( a, b, c \) (which can be the same), there exists a triangle with side lengths \( f(a), f(b), f(c) \), determine the range of values for \( k \).

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