
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 the function $f(x)=\frac{x+1}{x}$, and the function $y=g\left(x\right)-1$ is an odd function defined on $\mathbb{R}$. If the graphs of $f\left(x\right)$ and $g\left(x\right)$ intersect at four points $A(x_{1}, y_{1})$, $B(x_{2}, y_{2})$, $C(x_{3}, y_{3})$, $D(x_{4}, y_{4})$, then $y_{1}+y_{2}+y_{3}+y_{4}=\_\_\_\_\_\_$.

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