
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 $f(x) = e^x(ax^2 + bx + 1)$, where $a, b \in \mathbb{R}$, and the derivative of $f(x)$ is denoted by $f'(x)$. It is also known that $f'(-1) = 0$.  
(I) If $b = 1$, find the equation of the tangent to the curve $y = f(x)$ at the point $(0, f(0))$.  
(II) If the minimum value of the function $f(x)$ on the interval $[-1, 1]$ is $0$, find the value of $b$.

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