
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 $y=2x+m$ intersects the circle $x^2+y^2=1$ at points A and B. Taking the positive direction of the x-axis as the initial side, the angle with OA as the terminal side (where O is the origin) is $\alpha$, and the angle with OB as the terminal side is $\beta$. If $|AB|=\sqrt{3}$, find the value of $\sin(\alpha-\beta)$.

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