
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 $f\left(x\right)=\dfrac{x-a}{\ln x}$, where $a\in \mathbb{R}$.
- (Ⅰ) When $a=0$, find the monotonic intervals of the function $f\left(x\right)$.
- (Ⅱ) For any $x\in \left(1,+\infty \right)$, if $f\left(x\right) \gt \sqrt{x}$ always holds, find the range of $a$.

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