
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 domain of the function $f(x)$ is $\mathbb{R}$ and $$\frac{f'(x)}{2} - f(x) > 2,$$ if $f(0) = -1$, then the solution set of the inequality $$\frac{f(x) + 2}{e^{2x}} > 1$$ is __________.

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