
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]


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Given a function $f(x)$ defined on $\mathbb{R}$ with its derivative denoted as $f''(x)$, and it is known that $f(x) + f''(x) > 1$, $f(1) = 0$, find the solution set of the inequality $f(x) - 1 + \frac{1}{{e}^{x-1}} \leqslant 0$.

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