
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
Selected Exercise $(4-5)$: Inequality Lecture

Given the function $f(x)=|x-1|+|x-a|$.

$(1)$ If $a=2$, solve the inequality $f(x)\geqslant 2$;

$(2)$ If $a > 1$, for all $x\in R$, $f(x)+|x-1|\geqslant 1$, find the range of values for the real number $a$.

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