
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 $f(x)=|2x+ \frac{1}{2}|+a|x- \frac{3}{2}|$.
(I) When $a=-1$, solve the inequality $f(x)\leqslant 3x$;
(II) When $a=2$, if the solution set of the inequality $2f(x)+1 < |1-b|$ regarding $x$ is an empty set, find the range of values for the real number $b$.

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