
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 curve $y=(ax-1)e^{x}$, its tangent line at point $A(x_{0},y_{1})$ is $l_{1}$, and the curve $y=(1-x)e^{-x}$ has a tangent line $l_{2}$ at point $B(x_{0},y_{2})$. If there exists $x_{0}∈[0, \frac {3}{2}]$ such that $l_{1}⊥l_{2}$, find the range of the real number $a$.

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