
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 $f(x)=x-1-a\ln x$, $g(x)=\frac{ex}{e^{x}}$, $a < 0$, and for any $x\_1$, $x\_2\in[3,4](x\_1\neq x\_2)$, $\lvert f(x\_1)-f(x\_2)\rvert < \lvert \frac{1}{g(x\_1)}-\frac{1}{g(x\_2)}\rvert$ holds true, find the range of the real number $a$.

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