
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 $f(x) = ax - b\ln x$, the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ is $y = x + 1$.

1. Determine the intervals on which the function $f(x)$ is monotonic.
2. For any $x \geq 1$, if $f(x) \geq kx$ always holds, find the range of values for $k$.

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