
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
In the rectangular coordinate system xOy, points A($x\_1$, $y\_1$) and B($x\_2$, $y\_2$) are two points on the unit circle $x^2+y^2=1$, and $|AB|=1$. Determine the angle $\angle AOB$ and the maximum value of $|y\_1+2|+|y\_2+2|$.

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