
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 $f(x)$ is a function defined on $R$, and $f(x+1)$ is an odd function. If the function $g(x)=\ln(\sqrt{x^2-2x+2}-x+1)$ has $5$ intersection points with the graph of the function $f(x)$, with the abscissas from left to right being $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, $x_{5}$, calculate the sum of $x_1, x_2, x_3, x_4, x_5$.

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