
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 $f(x)=a•{3^x}+\frac{1}{{{3^{x-1}}}}$ is an even function with the domain of $R$.  
$(1)$ Find the value of $a$;  
$(2)$ If $g\left(x\right)=9^{x}+9^{-x}+mf\left(x\right)+m^{2}-1$, find the minimum value of the function $g\left(x\right)$.

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