
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 $f(x) = x^2 + 2ax + 3$, where $x \in [-2, 2]$

(1) When $a = -1$, find the maximum and minimum values of the function $f(x)$;  
(2) Let the minimum value of $f(x)$ in the interval $[-2, 2]$ be denoted as $g(a)$, find the expression for $g(a)$.

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