
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 $f(x) = (x^2 + ax + a)e^{-x}$, where $a$ is a constant and $e$ is the base of the natural logarithm:

1. Find $f'(2)$ when $a = 0$.
2. Determine the range of values for $a$ such that $f(x)$ attains a minimum value at $x = 0$.
3. Under the conditions of part 2, let $g(a)$ be the function formed by the maximum values of $f(x)$. Replace $a$ with $x$ and determine whether the curve $y = g(x)$ can be tangent to the line $3x - 2y + m = 0$ (where $m$ is a fixed constant), and explain your reasoning.

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