
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 functions $f(x)=|x+1|$ and $g(x)=2|x|+a$.  
(I) When $a=0$, solve the inequality $f(x)\geqslant g(x)$.  
(II) If there exists $x\in\mathbb{R}$ such that $f(x)\geqslant g(x)$ holds, find the range of the real number $a$.

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