
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 function f(x) = 4x^2 - 4ax + (a^2 - 2a + 2).
(1) If a = 2, find the range of the function y = f(x) in the interval [1, 2].
(2) If the function y = f(x) has a minimum value of 3 in the interval [0, 2], find the value of a.

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