
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 $$f(x)= \frac {\ln(x)}{x}- \frac {k}{x}$$ (where $k\in \mathbb{R}$),

1. If the maximum value of the function $f(x)$ is $h(k)$, and $k \neq 1$, compare the magnitude between $h(k)$ and $\frac {1}{e^{2k}}$.
2. If the inequality $$x^{2}f(x)+ \frac {1}{x+1}\geq 0$$ and $$k\geq -x+4\sqrt{x}-\frac{15}{4}$$ are both always satisfied on the interval $[1, +\infty)$, find the range of values for the real number $k$.

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