
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 $a$ is a real number, the function is $f(x) = a \ln x + x^2 - 4x$.
(1) When $a=1$, find the equation of the tangent line to the function $f(x)$ at $x=1$;
(2) Let $g(x) = (a-2)x$. If $\forall x \in [\frac{1}{e}, e]$, such that $f(x) \geq g(x)$ holds, find the range of values for the real number $a$.
(3) Definition: If there exist two points $A$ and $B$ on the graph of the function $m(x)$, and the midpoint of the line segment $AB$ is $P(x_0, y_0)$, if the tangent line $l$ to the function $m(x)$ at point $Q(x_0, m(x_0))$ is parallel or coincident with the line $AB$, then the function $m(x)$ is called a "mean-value average function," and the tangent line $l$ is called the "mean-value average tangent line" of the function $m(x)$. Determine whether the function $f(x)$ is a "mean-value average function." If it is, identify the number of "mean-value average tangent lines" of the function $f(x)$; if not, explain the reason.

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