
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 two points $A$ and $B$ in the Cartesian coordinate system that satisfy the following conditions: (1) Both points $A$ and $B$ are on the graph of the function $f(x)$; (2) Points $A$ and $B$ are symmetric about the origin. If such points exist, they are called a "sister pair" of function $f(x)$. The sister pair $(A, B)$ and $(B, A)$ are considered the same. Given the function $f(x) = \begin{cases} x^2 + 2x & (x < 0) \\ \frac{2}{e^x} & (x \geq 0) \end{cases}$, determine the number of "sister pairs" for $f(x)$.

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