
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 that $\alpha$ is an angle in the fourth quadrant in the Cartesian coordinate system $xOy$, the terminal side of angle $\alpha$ intersects the unit circle $O$ at point $P(x_{0}, y_{0})$, and $\cos(\alpha - \frac{\pi}{3}) = -\frac{\sqrt{3}}{3}$, find the value of $y_{0}$.

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