
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 $f(x) = \ln{x} - ax - b$, where $a, b \in \mathbb{R}$,
(Ⅰ) If the function $f(x)$ attains an extremum of 1 at $x=1$, determine the values of $a$ and $b$.
(Ⅱ) Discuss the monotonicity of the function $f(x)$ on the interval $(1, +\infty)$.
(Ⅲ) For any two points $A(x_1, y_1)$ and $B(x_2, y_2)$ on the graph of the function $f(x)$, with $x_1 < x_2$, the inequality $f'(x_0) < k$ always holds, where $k$ is the slope of line $AB$, $x_0 = \lambda x_1 + (1 - \lambda) x_2$, and $0 < \lambda < 1$. Determine the range of $\lambda$.

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