
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 $\sin\alpha$ is a root of the equation $5x^2 - 7x - 6 = 0$. Calculate the value of 
$$\frac{\sin(-\alpha - \frac{3\pi}{2}) \cdot \sin(\frac{3\pi}{2} - \alpha) \cdot \tan^2(2\pi - \alpha)}{\cos(\frac{\pi}{2} - \alpha) \cdot \cos(\frac{\pi}{2} + \alpha) \cdot \cot(\pi - \alpha)}.$$

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