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

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

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

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