
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 functions $f\left(x\right)=\log _{a}(1+x)$ and $g\left(x\right)=\log _{a}(1-x)$, where $a \gt 0$ and $a\neq 1$.<br/>$(1)$ Find the domain of the function $f\left(x\right)\cdot g\left(x\right)$ and determine the parity of $f\left(x\right)\cdot g\left(x\right)$;<br/>$(2)$ If $f(1)+g({\frac{1}{4}})＜1$, find the range of values for $a$.

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