
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 $y = f(x)$ ($x \in \mathbb{R}$) with its derivative $f'(x)$, $f(0) = 2$, and $f(x) + f'(x) > 1$, determine the solution set for the inequality $e^{x}f(x) > e^{x} + 1$.

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