
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 three sets A, B, and C where A = {x | x^2 - 3x + 2 = 0}, B = {x | x^2 - ax + (a-1) = 0}, and C = {x | x^2 - mx + 2 = 0}, with the conditions A ∪ B = A and A ∩ B = C, find the real numbers a and m.

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