
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 $f(x) = \frac{\ln(1+x)}{x}$.
(1) Determine the monotonicity of the function $f(x)$ on the interval $(0, +\infty)$ and explain the reasoning;
(2) If the function $f(x)$ always satisfies $f(x) < \frac{1-ax}{1+x}$ within its domain, determine the set of all possible values of $a$.

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