
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
Define a function $f(x)$ on $\mathbb{R}$, where $f'(x)$ is its derivative, and it satisfies $f(x)+f'(x) > 2$, $f(1)=2+ \frac{4}{e}$. Find the solution set of the inequality $e^{x}f(x) > 4+2e^{x}$.

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