
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 $f(x)=x^{3}+3ax^{2}+3x+1$.  
(I) Discuss the monotonicity of $f(x)$ when $a=-\sqrt{2}$.  
(II) If $x\in[2,+\infty)$ and $f(x)\geqslant 0$, find the range of $a$.

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