
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 function $f(x)$ is an even function, ${f'}(x)$ is the derivative of $f(x)$, and $f'(-x)-f'(x)=2\sqrt{2}\sin x$. When $x > -\frac{3\pi}{2}$, $f(x) \leq e^{x+\frac{\pi}{4}} - \frac{\pi}{4}$, write down a function that satisfies the conditions: $f(x)=$____.

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