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

1. If the slope of the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$ is 10, find the maximum value of the function $f(x)$.
2. If the inequality $x^2 f(x) + \frac {1}{x+1} \geq 0$ together with $k \geq \frac {1}{2} x^2 + (e^2 - 2)x - e^x - 7$ are always true on the interval $[1, +\infty)$, determine the range of the real number $k$.

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