
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 \( f(x) = \frac{x^4 + k x^2 + 1}{x^4 + x^2 + 1} \), where \( k \) and \( x \) are real numbers,
1. Find the maximum and minimum values of \( f(x) \);
2. Find all real numbers such that for any three real numbers \( a, b, \) and \( c \), there exists a triangle with side lengths \( f(a), f(b), \) and \( f(c) \).

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