
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 $f(x)=\left\{{\begin{array}{l}{x+4e, x\leq 0}\\{\frac{{{e^x}}}{{{x^2}}}, x>0}\end{array}}\right.$ (where $e$ is the base of the natural logarithm), if there exist $x_{1}\leq 0$ and $x_{2} > 0$ such that $f(x_{1})=f(x_{2})$, determine the range of $x_{1}f(x_{2})$.

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