
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
The line $y=3x$ and the circle $x^2+y^2=1$ intersect at points A and B. Taking the positive x-axis as the initial side, and OA, OB as the terminal sides, the angles are respectively $\alpha$ and $\beta$. The value of $\sin(\alpha+\beta)$ is \_\_\_\_\_\_.

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