
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 the function $f(x)$ has a domain of $(0, +\infty)$, $f(1) = e$, and for any $x_{1}$, $x_{2} \in (0, +\infty)$, when $x_{2} > x_{1}$, it holds that $\frac{{f(x_{1}) - f(x_{2})}}{{x_{1}x_{2}}} > \frac{{e^{x_{2}}}}{{x_{1}}} - \frac{{e^{x_{1}}}{{x_{2}}}}$ (where $e$ is the base of the natural logarithm). If $f(\ln a) > 2e - a\ln a$, then the range of real number $a$ is ____.

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