
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 the functions $f(x)=e^{x-1}+x-2$ (where $e$ is the base of the natural logarithm) and $g(x)=x^{2}-ax-a+3$. If there exist real numbers $x_{1}$ and $x_{2}$ such that $f(x_{1})=g(x_{2})=0$ and $|x_{1}-x_{2}|\leqslant 1$, then the range of values for the real number $a$ is \_\_\_\_\_\_.

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