
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 that the derivative of the function $g(x)$ on $R$ is ${g'}(x)$, for all $x\in R$, $\frac{{g(x)}}{{g({-x})}}={e^{2x}}$. When $x\geqslant 0$, ${g'}(x) \gt g(x)$. If $g(3m-2)\geqslant e^{m-3}g(2m+1)$, then the range of real number $m$ is ______.

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