
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
If the terminal side of angle $\alpha$ lies on the line $y=\sqrt{3}x$, the terminal side of angle $\beta$ intersects the unit circle at point $(\frac{1}{2},m)$, and $\sin \alpha \cdot \cos \beta < 0$, then $\cos \alpha \cdot \sin \beta=$ _____.

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