
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 Cartesian coordinate system $xOy$, suppose the terminal side of an obtuse angle $\alpha$ intersects the circle $O: x^2+y^2=4$ at point $P(x_1, y_1)$. Point $P$ moves clockwise along the circle for an arc length of $\frac{2\pi}{3}$ units to reach point $Q$, with coordinates $(x_2, y_2)$. Determine the range of values for $y_1+y_2$.

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