
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 $f\left( x \right)={e}^{3ax}$ $\left( a\in R \right)$, its graph $C$ has a tangent line at point $P\left( 1,f\left( 1 \right) \right)$ with a slope of $e$. Let $g\left( x \right)=kx+b$ $\left( k,b\in R,k\ne 0 \right)$ be an odd function with the graph $l$.

(1) Find the values of real numbers $a$ and $b$.
(2) When $x\in \left( -2,2 \right)$, graph $C$ is always above graph $l$. Find the range of real number $k$.

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