
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 $f(x)=\ln (x+1)- \frac{ax}{x+1}-x$, where $a\in R$.
(I) Find the monotonic intervals of the function $f(x)$ when $a > 0$.
(II) If there exists $x > 0$ such that $f(x)+x+1 < - \frac{x}{x+1}$ ($a\in Z$) holds, find the minimum value of $a$.

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