
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 $f(x)=\ln x-x+1+a$ and $g(x)=x^{2}e^{x}$ (where $e$ is the base of the natural logarithm), if for any $x\_1\in[\frac{1}{e},1]$ there always exists an $x\_2\in[0,1]$ such that $f(x\_1)=g(x\_2)$, then the range of values for the real number $a$ is $\_\_\_\_\_\_\_\_\_.$

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