
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 $f(x)=x+\frac{a}{x}$, where $a\in \mathbb{R}$.  
$(Ⅰ)$ If the zero point of $y=f(x)$ exists on $(0,+\infty)$, find the range of real number $a$.  
$(Ⅱ)$ If the inequality $f(x)\geqslant a$ holds for all $x\in [2,+\infty)$, find the range of real number $a$.

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