
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 functions $f(x)=\frac{\ln x}{x}$ and $g(x)=\frac{m}{x}+\frac{1}{2}$ where $m\in\mathbb{R}$.

1. Find the equation of the tangent line to the curve $y=g(x)$ at $x=1$ when $m=1$.
2. Determine the monotonic intervals of $f(x)$ and compare the sizes of $2017^{\frac{1}{2017}}$ and $2016^{\frac{1}{2016}}$.
3. If the inequality $bf(x)>g(x)$ holds for any positive real number $b$ in the interval $[1,e]$, find the range of values for the real number $m$. (Note: $e=2.71828...$)

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