
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 $f(x)=|x+a|+|x-2|$ with a domain of all real numbers $\mathbb{R}$.
(I) Solve the inequality $f(x) > 9$ when $a=5$;
(II) Let $A$ be the solution set of the inequality $f(x)\leqslant |x-4|$ and $B=\{x\in\mathbb{R}||2x-1|\leqslant 3\}$. If $A\cup B=A$, find the range of values for the real number $a$.

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