
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 $f(x)$ (where $x \in \mathbb{R}$) satisfies $f(-x) = 4 - f(x)$, if the graph of the function $y=\frac{2x+1}{x}$ intersects with the graph of $y=f(x)$ at the points $(x_1, y_1), (x_2, y_2), \ldots, (x_m, y_m)$, then calculate the sum $\sum_{i=1}^{m} (x_i + y_i)$.

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