
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 a function \( f(x) \) such that \( f(2-x)=2-f(x) \) for all \( x \in \mathbf{R} \), the intersection points of the graphs of the functions \( y=\frac{x}{x-1} \) and \( y=f(x) \) are \((x_i, y_i)\) for \(i=1, 2, \cdots, n\). Find \( \sum_{i=1}^{n}(x_i + y_i) = \) ________.

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