
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 real numbers $x_1$, $x_2$, $y_1$, $y_2$ satisfying: $x_1^2+y_1^2=1$, $x_2^2+y_2^2=1$, $x_1x_2+y_1y_2=\frac{1}{2}$, find the maximum value of $\frac{|x_1+y_1-1|}{\sqrt{2}} + \frac{|x_2+y_2-1|}{\sqrt{2}}$.

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