
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 point $P\left(-\sqrt{3}, y\right)$ where $y > 0$ lies on the terminal side of angle $\alpha$, and $\sin \alpha = \frac{\sqrt{3}}{4}y$, find the value of $\cos \alpha =$ $\_\_\_\_\_\_\_\_\_\_$

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