
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 $f(x)=a\ln x$ and $g(x)=(a+2)x-x^{2}$, if there exists $x_0 \in [\frac{1}{e}, e]$ such that $f(x_{0})\leqslant g(x_{0})$ holds, then find the range of the real number $a$.

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