
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
Let the constant $a\in \mathbb{R}$, and the sets $A=\left\{ x|\left( x-1 \right)\left( x-a \right)\geqslant 0 \right\}$, $B=\left\{ x|x\geqslant a-1 \right\}$. If $A\cup B=\mathbb{R}$, determine the range of values for $a$.

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