
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 $f(x)$ defined on $\left[-4,4\right]$ is ${f'}\left(x\right)$, and it satisfies ${f'}\left(x\right) \gt f\left(x\right)$. If $e^{x-1}f\left(1+x\right)-f\left(2x\right) \lt 0$, then the range of $x$ is ______.

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