
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
If $f(x) = x - 1 - a \ln x$ $(a \in \mathbb{R})$ and $g(x) = \frac {e^{x}}{x}$:
1. Find the extremum of $f(x)$ when $a = \frac{1}{e}$.
2. When $a < 0$ and for any $x_1, x_2 \in [4, 5]$ ($x_1 \neq x_2$), it always holds that $|f(x_1) - f(x_2)| < |g(x_1) - g(x_2)|$. Find the range of $a$.

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