
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
Consider the function $f(x)=|x+ \sqrt {1-a}|-|x- \sqrt {a}|$.  
(1) When $a=0$, solve the inequality $f(x)\geqslant 0$;  
(2) If for any $a\in[0,1]$, the inequality $f(x)\geqslant b$ has solutions with respect to $x$, find the range of values for the real number $b$.

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