
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 $f(x)=|2x-a|-|x-2|$.<br/>$(Ⅰ)$ When $a=-2$, find the solution set of the inequality $f(x)\leqslant 4$;<br/>$(Ⅱ)$ If the inequality $f(x)\geqslant 3a^{2}-3|2-x|$ holds for all $x$, find the range of values for $a$.

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