
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 $f(x)=\frac{a\ln x}{x}+b\ (a,b\in\mathbb{R})$, its graph has a tangent line at the point $(1,f(1))$ with the equation $y=x-1$.

(I) Find the values of the real numbers $a$ and $b$ and the monotonic intervals of the function $f(x)$;

(II) Compare $x\_1+x\_2$ with $2e\ (e$ is the base of the natural logarithm$)$ when $f(x\_1)=f(x\_2)\ (x\_1\neq x\_2)$.

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