
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 $f\left(x\right)=-\ln x+\frac{a}{x}-ex+4$, $g\left(x\right)=\frac{1}{3}{x^3}-{x^2}+2$. If for all $x_{1}\in \left(0,1\right]$, there exists $x_{2}\in \left[-1,1\right]$, such that $g(x_{2})\geqslant f(x_{1})$, then the range of $a$ is ____.

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