
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
Given equations (1) $\cos \alpha - \sin \theta + \sin \alpha \sin \theta = 0$ and (2) $\cos \alpha + \cos \theta - \sin \alpha \cos \theta = 0$, with $\alpha \in \left(-\frac{\pi}{2}, 0\right)$:

(I) Find the value of $\sin \alpha$;

(II) If $-\frac{\pi}{2} < \alpha - \beta < 0$ and $\cos \left(\alpha - \beta\right) = \frac{2}{3}$, find the value of $\sin \beta$.

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