
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 function $f(x)= \frac{x^{2}+kx+1}{x^{2}+1}$.

(I) If when $x > 0$, the minimum value of $f(x)$ is $-1$, find the value of the real number $k$;

(II) If for any ${x}_{1},{x}_{2},{x}_{3}\in(0,+\infty)$, there always exists a triangle with side lengths $f({x}_{1}),f({x}_{2}),f({x}_{3})$, find the range of values for the real number $k$.

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