
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 $f(x) = \ln x + \frac{a}{x}$, where $a \in \mathbb{R}$, and the tangent line of the function $f(x)$ at $x=1$ is parallel to the line $2x-y=0$.
(Ⅰ) Find the value of the real number $a$;
(Ⅱ) If there exists a point $x_0$ in the interval $[1,e]$ ($e=2.718...$) such that $x_0 + \frac{1}{x_0} < mf(x_0)$ holds, find the range of values for the real number $m$.

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