
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 $f(x)=|2x-1|$.

(I) If the solution set of the inequality $f\left( x+\frac{1}{2} \right)\leqslant 2m+1(m > 0)$ is $[-2,2]$, find the value of the real number $m$;

(II) If the inequality $f(x)\leqslant {{2}^{y}}+\frac{a}{{{2}^{y}}}+|2x+3|$ holds for any real number $x$ and $y\in R$, find the minimum value of the real number $a$.

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