
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 $f(x)=|x-a|+|x-\frac{1}{2}|,x\in\mathbb{R}$
(I) When $a=\frac{5}{2}$, solve the inequality $f(x)\leqslant x+10$;
(II) Find the range of values of the real number $a$ for which the inequality $f(x)\geqslant a$ holds for all $x$ in $\mathbb{R}$.

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