
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 $a \gt 0$ and $a\neq 1$, the function $f(x)=\frac{{{a^x}-{a^{-x}}}{{a^x}+{a^{-x}}}+b$ is a monotonically decreasing function on $R$, and satisfies two of the following three conditions: ① the function $f(x)$ is an odd function; ② $f(1)=-\frac{3}{5}$; ③ $f({-1})=-\frac{3}{5}$. <br/> $(1)$ Choose the numbers of the two selected conditions as ______, and determine $a=$______, $b=\_\_\_\_\_\_.$ <br/> $(2)$ In case (1), for the equation $f(x)=m-4^{x}$, there are two distinct real roots in $x\in \left[-1,1\right]$. Find the range of values for $m$.

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