
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 an even function $f\left(x\right)$ defined on $R$ satisfies $f\left(x\right)=f\left(-x+4\right)$, $f\left(2024\right)=\frac{1}{{e}^{2}}$, if $f\left(x\right)-{f'}\left(x\right) \gt 0$, then the solution set of the inequality $f\left(x+2\right) \gt e^{x}$ is ______.

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