
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 $f(x)=|x-\frac{5}{2}|+|x-a|$, where $x\in\mathbb{R}$:
(I) Find the solution set of the inequality $f(x)\geqslant 4$ when $a=-\frac{1}{2}$;
(II) Find the maximum value of the real number $a$ such that the inequality $f(x)\geqslant a$ holds true for all $x\in\mathbb{R}$.

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