
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 function $f(x)=(2-a)(x-1)-2\ln x$, $g(x)=xe^{1-x}$ ($a\in\mathbb{R}$, $e$ is the base of the natural logarithm), for any given $x_{0}\in(0,e]$, determine the range of values for $a$ such that there always exist two different $x_{i}(i=1,2)$ in $(0,e]$ satisfying $f(x_{i})=g(x_{0})$.

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