
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 ${f'}\left(x\right)$ of the function $f\left(x\right)$ satisfies ${f'}\left(x\right) \gt f\left(x\right)$ holds for all $x$ in $R$, then the solution set of the inequality $e^{2}f\left(2x-1\right)-e^{3x}f\left(1-x\right) \gt 0$ is ______.

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