
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 $f(x)= \frac {x^{2}+1}{x^{2}+2kx+1}$ $(k > 0)$.  
(1) If for any $x\in(0,+\infty)$, the inequality $f(x)\geqslant \frac {1}{2}$ always holds, find the range of values for the real number $k$.  
(2) If for any $a$, $b$, $c\in\mathbb{R}^{+}$, there always exists a triangle with sides of lengths $\frac {1}{f(a)}$, $\frac {1}{f(b)}$, $\frac {1}{f(c)}$, find the range of values for the real number $k$.

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