
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 $f\left(x\right)={x}^{3}-3ax+b\left(a,b\in R\right)$ takes the extreme value $1$ at $x=-1$.

(1) Find the values of $a$ and $b$;

(2) Find the equation of the tangent line of the function $g\left(x\right)=f\left(x\right)+{e}^{2x-1}$ at $x=1$.

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