
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 $a > 0$, and define the functions $f(x) = x + \frac{a^2}{x}$, $g(x) = x - \ln(x)$. If for any $x_1 \in (0, +\infty)$ and any $x_2 \in [1, e]$, the inequality $f(x_1) \geq g(x_2)$ always holds, then find the range of values for the real number $a$.

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