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

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