
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 $f(x) = x - 1 - a \ln x$.
(I) If $a = 2$, find the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$;
(II) Discuss the monotonicity of $f(x)$;
(III) If $a < 0$, and for any $x_1, x_2 \in (0, 1]$, it always holds that $|f(x_1) - f(x_2)| \leq 4 \left| \frac{1}{x_1} - \frac{1}{x_2} \right|$, find the range of $a$.

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