
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 $f(x) = \frac{1-a}{2}x^2 + ax - \ln{x}$, where $a \in \mathbb{R}$:
1. Find the extreme values of the function $f(x)$ when $a = 1$.
2. If for any $a \in (4, 5)$ and any $x_1, x_2 \in [1, 2]$, the inequality $\frac{a-1}{2}m + \ln{2} > |f(x_1) - f(x_2)|$ holds, find the range of values for the real number $m$.

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