
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 vertex is at the origin, and the initial side is on the positive half of the $x$-axis for angles $\alpha$ and $\beta$. The terminal sides of $\alpha$ and $\beta$ intersect with the unit circle centered at the origin at points $A$ and $B$, respectively. If $\alpha=30^{\circ}$ and $\beta=60^{\circ}$, then the length of chord $AB$ is __________.

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