
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 $\cos \alpha$ is a root of the equation $3x^2 - x - 2 = 0$ and $\alpha$ is an angle in the third quadrant, find the value of $\frac{\sin (-\alpha + \frac{3\pi}{2}) \cos (\frac{3\pi}{2} + \alpha) \tan^2 (\pi - \alpha)}{\cos (\frac{\pi}{2} + \alpha) \sin (\frac{\pi}{2} - \alpha)}$.

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