
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
The function $f(x)=\ln (9^{x}+3^{x}-a)$.  
$(1)$ If the domain of $f(x)$ is $R$, find the range of real number $a$.  
$(2)$ When $a=0$, $g(x)$ is an odd function with domain $R$, and for $x>0$, $g(x)=e^{f(x)}-9^{x}$. If the equation $\frac{g(x^{2}-2tx+3)}{g(x)}=|g(x)|$ always has two distinct real roots, find the range of $t$.

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