
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 $f(x) = \ln x - a(x - 1)$, where $a \in \mathbb{R}$.
1. Find the equation of the tangent line to the function $f(x)$ at the point $(1, f(1))$.
2. When $a = 1$, find the extreme points and the corresponding extreme values of $f(x)$.
3. When $x \geq 1$, $f(x) \leq \frac{\ln x}{x + 1}$ always holds true, determine the range of values for $a$.

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