
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
Let the curve $y=(ax-1)e^x$ have a tangent line $l_1$ at the point $A(x_0, y_1)$, and the curve $y= \frac {1-x}{e^{x}}$ have a tangent line $l_2$ at the point $B(x_0, y_2)$. If there exists an $x_0$ within the interval $[0, \frac{3}{2}]$ such that $l_1$ is perpendicular to $l_2$, then the range of the real number $a$ is ________.

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