
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 the function $f(x)=\ln (x+1)+a(x^{2}-x)$, where $a\in \mathbb{R}$,  
(I) Discuss the number of extreme points of the function $f(x)$ and explain the reason;  
(II) If $\forall x > 0$, $f(x)\geqslant 0$ holds, find the range of values for $a$.

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