
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
Let $a \gt 0$, $f(x)=x+\frac{a^2}{x}$, $g(x)=x-\ln x$. If $f(x_{1})\geqslant g(x_{2})$ holds for any $x_{1}$, $x_{2}\in \left[1,e\right]$, then the range of real number $a$ is ____.

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