
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 $f(x) = x^2 - 2ax + a^2 - 1$.
1. If $f(1) = 3$, find the value of the real number $a$;
2. If the function $f(x)$ is monotonic in the interval $[0, 2]$, find the range of values for the real number $a$;
3. When $x \in [-1, 1]$, find the minimum value of the function $f(x)$, denoted as $g(a)$.

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