
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
The domain of the function $f(x)$ is $(-\infty, 1) \cup (1, +\infty)$, and $f(x + 1)$ is an odd function. When $x > 1$, $f(x) = 2x^2 - 12x + 16$. Find the sum of the x-coordinates of all the points of intersection between the line $y=2$ and the graph of the function $f(x)$.

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