
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 $f(x)$ $(x \in \mathbb{R})$ that satisfies the equation $f(-x) = 8 - f(4 + x)$, and another function $g(x) = \frac{4x + 3}{x - 2}$. If the graph of $f(x)$ has 168 intersection points with the graph of $g(x)$, denoted as $P_i(x_i, y_i)$ $(i = 1,2, \dots, 168)$, calculate the value of $(x_{1} + y_{1}) + (x_{2} + y_{2}) + \dots + (x_{168} + y_{168})$.

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