
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 $f(x) = e^{3ax}$ (where $a \in \mathbb{R}$), the slope of the tangent to its graph $C$ at point $P(1, f(1))$ is $e$. Let the odd function $g(x) = kx + b$ (where $k, b \in \mathbb{R}$, $k \neq 0$) be represented by line $l$.
(1) Find the values of real numbers $a$ and $b$.
(2) When $x \in (-2, 2)$, graph $C$ is always above line $l$. Find the range of values for real number $k$.

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