
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 $a > 0$, the function $f(x)=x+ \frac{a^{2}}{x}$, $g(x)=x-\ln x$, if for any $x_{1} \in \mathbb{R}$, any $x_{2} \in [1,e]$, it holds that $f(x_{1}) \geqslant g(x_{2})$, then the range of the real number $a$ is ______.

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