
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 function $f(x) = a \ln x - ax - 3 (a \in \mathbb{R})$,
(1) Find the monotonic intervals of the function $f(x)$ when $a > 0$;
(2) If the tangent line to the graph of the function $y = f(x)$ at the point $(2, f(2))$ has a slope of $45^{\circ}$, and the function $g(x) = \frac{1}{2}x^2 + nx + mf'(x) (m, n \in \mathbb{R})$ takes an extreme value only at $x = 1$, where $f'(x)$ is the derivative of $f(x)$, find the range of values for $m$.

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