
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 sets $A=\{0,2\}$ and $B=\{x|\left(ax-1\right)\left(x-1\right)(x^{2}-ax+1)=0,x\in R\}$, define $A$※$B=\left\{\begin{array}{l}{|A|-|B|,|A|\geq|B|}\\{|B|-|A|,|A|<|B|}\end{array}\right.$. If $A$※$B=1$, find the set of all possible values of the real number $a$.

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