
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 $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$ are points on the circle $\odot O: x^{2}+y^{2}=1$, and $|AB|=1$. Determine the maximum value of $\left|x_{1}+y_{1}-1\right| + \left|x_{2}+y_{2}-1\right|$.

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