
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 sets $A=\{x|x^2-3x+2=0\}$, $B=\{x|x^2-ax+a-1=0\}$, and $C=\{x|x^2-mx+2=0\}$. If $A \cup B = A$ and $A \cap C = C$, find the range of values for the real numbers $a$ and $m$.

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