
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
Let $f(x) = \ln(x+1) - \frac{ax}{x+1}$ where $a \in \mathbb{R}$.
(I) If $f(0)$ is the minimum value of $f(x)$, find the value of $a$;
(II) If $f(x) > 0$ holds for all $x \in (0,+\infty)$, find the maximum value of $a$.

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