
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 that the function $f(x) = \frac{1-x}{ax} + \ln x$ is increasing on the interval $(1, +\infty)$ and that $a > 0$,  
(1) Determine the range of values for $a$;  
(2) Find the maximum value of the function $g(x) = \ln(1+x) - x$ on the interval $[0, +\infty)$.

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