
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 equation in terms of $x$, $x^2 - 2mx + 3 + 4m^2 - 6 = 0$, with roots $\alpha$ and $\beta$, find the maximum and minimum values of $(\alpha-1)^2 + (\beta-1)^2$.

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