
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 $a=1$, find the range of $f(x)$ on the closed interval $[0, 2]$.  
(2) If $f(x)$ has a minimum value of 3 on the closed interval $[0, 2]$, find the value of the real number $a$.

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