
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 $f(x) = e^x - kx^2$, where $x \in \mathbb{R}$.

(1) Let the function $g(x) = f(x)(x^2 - bx + 2)$, when $k=0$, if the function $g(x)$ has an extreme value, find the range of the real number $b$.

(2) If $f(x)$ is monotonically increasing on the interval $(0, +\infty)$, find the range of $k$.

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