
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 $f(x)=x\ln (x+1)+\left( \frac {1}{2}-a\right)x+2-a$, where $a\in \mathbb{R}$.  
(I) When $x > 0$, find the monotonic interval of the function $g(x)=f(x)+\ln (x+1)+ \frac {1}{2}x$;  
(II) When $a\in \mathbb{Z}$, if there exists $x\geqslant 0$ such that the inequality $f(x) < 0$ holds, find the minimum value of $a$.

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