
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 the functions be $f(x)= \frac {e^{2}x^{2}+1}{x}$ and $g(x)= \frac {e^{2}x}{e^{x}}$. For any $x_{1}$, $x_{2} \in (0,+\infty)$, the inequality $\frac {g(x_{1})}{k} \leqslant \frac {f(x_{2})}{k+1}$ always holds. Then, the range of values for the positive number $k$ is \_\_\_\_\_\_.

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