
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 a function $f(x) = \frac{mx}{\ln x}$, the tangent line of the curve $y = f(x)$ at the point $(e^2, f(e^2))$ is perpendicular to the line $2x+y=0$ (where $e$ is the base of natural logarithms).  
(1) Find the explicit expression of $f(x)$ and the interval where it is monotonically decreasing;  
(2) If there exists $x_0 \in [e, +\infty)$ such that the function $g(x)=ae^{\ln x}+ \frac{1}{2}x^{2} - \frac{a+e}{2}\ln x f(x) \leq a$ holds, find the range of values for the real number $a$.

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