
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 functions $f(x)=x+\frac{a^{2}}{x}$ and $g(x)=x+\ln x$, where $a > 0$,
(Ⅰ) when $a=2$, find the interval over which the function $f(x)$ is monotonically decreasing;
(Ⅱ) if for any $x_{1}, x_{2} \in [1, e]$ (where $e$ is the base of natural logarithms), the inequality $f(x_{1}) \geqslant g(x_{2})$ holds, find the range of the real number $a$.

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