
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 that $a > 0$, let $f(x) = x + \frac{a^{2}}{x}$ and $g(x) = x - \ln{x}$. If for any $x\_1 \in (0, +\infty)$ and any $x\_2 \in [1, e]$, we have $f(x\_1) \geq g(x\_2)$, then the range of values for the real number $a$ is $\_\_\_\_\_\_\_\_$.

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