
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 $f(x) = \ln{x} - ax - 3$ where $a \in \mathbb{R}$ and $a \neq 0$.
1. Find the monotonic intervals of the function $f(x)$.
2. If the tangent line of the graph of the function $y = f(x)$ at the point $(2, f(2))$ has a slope of $45^{\circ}$, and for any $t \in [1, 2]$, the function $g(x) = x^3 + x^2[f'(x) + \frac{m}{2}]$ is not always monotonic on the interval $(t, 3)$, find the range of values for $m$.

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