
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 $f(x)=|x+ \sqrt {a}|-|x- \sqrt {1-a}|.$
$(I)$ When $a=1$, find the solution set of the inequality $f(x)\geqslant \dfrac {1}{2}$.
$(II)$ If for any $a\in[0,1]$, the solution set of the inequality $f(x)\geqslant b$ is empty, find the range of the real number $b$.

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