
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 $f\left(x\right)=|x-a^{2}|+|x-2a+1|$.<br/>$(1)$ When $a=2$, find the solution set of the inequality $f\left(x\right)\geqslant 4$;<br/>$(2)$ If $f\left(x\right)\geqslant 4$, find the range of values for $a$.

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