
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 a function $f(x)$ defined on $\left(-2,2\right)$ such that $f(x) + e^{4x}f(-x) = 0$, $f(1) = e^{2}$, and ${f'}(x)$ is the derivative of $f(x)$. When $x \in \left[0,2\right)$, ${f'}(x) > 2f(x)$, find the solution set of the inequality $e^{2x}f(2-x) < e^{4}$.

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