
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 $f(x) = (x^2 - x - 1)e^{ax}$ $(a \neq 0)$.

(1) Find the equation of the tangent line to the curve $y = f(x)$ at the point $A(0, f(0))$.
    
(2) When $a > 0$, if the inequality $f(x) \geq 0$ is valid for all $x \in [-\infty, +\infty)$, determine the range of values for the real number $a$.

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