
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 $f(x)=\frac{{2}^{x}-b}{{2}^{x}+1}(b∈R)$ is an odd function, real numbers $m$ and $n$ are both less than $1$, $e=2.71828\ldots$ is the base of the natural logarithm, and $lo{g}_{2}|m-b|+2e-1={e}^{2}$, $lo{g}_{2}|n-b|+4e-1=4{e}^{2}$, determine the relationship between $m$ and $n$.

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