
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 $e$ is a constant, $a > 0$, $b \in \mathbb{R}$), the derivative of the function $f(x)$ is denoted as $f'(x)$, and $f'(-1) = 0$.
1. If $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(0, f(0))$.
2. When $a > \frac{1}{5}$, if the maximum value of the function $f(x)$ in the interval $[-1, 1]$ is $4e$, try to find the values of $a$ and $b$.

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