
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 $f(x)=|2x-a|+|2x-1|$, where $a\in R$.

(I) When $a=3$, find the solution set of the inequality $f(x)\leqslant 6$ with respect to $x$;

(II) When $x\in R$, find the range of real number $a$ such that $f(x)\geqslant {{a}^{2}}-a-13$.

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