
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 $5x^{2}-7x-6=0$, and $\alpha$ is an angle in the third quadrant, calculate 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