
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 $f(-x) = 4 - f(x)$, and the function $g(x) = \frac{x - 2}{x - 1} + \frac{x}{x + 1}$. If the intersection points of the curves $y = f(x)$ and $y = g(x)$ are respectively $(x\_1, y\_1)$, $(x\_2, y\_2)$, $(x\_3, y\_3)$, ..., $(x\_m, y\_m)$, then $\sum\_{i=1}^{m} (x\_i + y\_i) =$\_\_\_\_\_\_\_ (Express the result using a formula containing $m$.)

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