
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
Calculate the value of the following expressions:

(1) Given that $\sin \alpha$ is a root of the equation $5x^{2}-7x-6=0$, and $\alpha$ is an angle in the third quadrant, compute $\frac{\sin (-\alpha - \frac{3}{2}\pi)\cos (\frac{3}{2}\pi - \alpha)}{\cos (\frac{\pi}{2} - \alpha)\sin (\frac{\pi}{2} + \alpha)} \cdot \tan^{2} (\pi - \alpha)$;

(2) $\frac{\sqrt{1 - 2\sin 40^{\circ}\cos 40^{\circ}}}{\cos 40^{\circ} - \sqrt{1 - \sin^{2}50^{\circ}}}$.

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