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

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