
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 $f\left( x \right)=\left| x-a \right|+\left| x-\frac{1}{2} \right|,x\in R$

(I) When $a=\frac{5}{2}$, solve the inequality $f\left( x \right)\leqslant x+10$;

(II) Find the range of real number $a$ such that the inequality $f\left( x \right)\geqslant a$ holds true for all $x$ in $R$.

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