
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 that the function $f(x) (x \in \mathbb{R})$ satisfies $f(-x) = 4 - f(x)$, if the intersection points of the graph of the function $y = \frac{2x + 1}{x}$ and $y = f(x)$ are $(x\_1, y\_1), (x\_2, y\_2), ..., (x\_m, y\_m)$, then $\sum\limits\_{i=1}^{m} (x\_i + y\_i) =$ \_\_\_\_\_\_.

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