
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 $f(x) = e^x - a(x + 1)$, where $a \in \mathbb{R}$.
1. Find the monotonic intervals and extreme values of the function $f(x)$.
2. Let $g(x) = f(x) + \frac{a}{e^x}$, and let $A(x_1, y_1)$ and $B(x_2, y_2)$ ($x_1 \neq x_2$) be any two points on the curve $y = g(x)$. If the slope of line $AB$ is always greater than the constant $m$ for any $a \leq -1$, find the range of $m$.

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