
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 $f(x) = \frac{x^2 + (a+2)x + a}{e^x}$ where $a \in \mathbb{R}$, and $g(x) = e^x f(x)$.

1. Find the range of values for the real number $a$ if the set $A = \{x | g(x) \leq 9, x \in [a, +\infty)\} \neq \emptyset$.
2. If $M$ and $N$ are the maximum and minimum values of $f(x)$, respectively, find the range of values for $\frac{M}{N}$.

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