
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 tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ has a slope of $10$, find the maximum value of the function $f(x)$.
(2) If the inequalities $x^2f(x)+\frac{1}{x+1}\geq 0$ and $k\geq\frac{1}{2}x^2+(e^2-2)x-e^x-7$ hold true for all $x\in[1,+\infty)$, find the range of values for the real number $k$.

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