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

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