
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 $cos\left( \frac{\pi}{6}-\alpha\right) = \frac{\sqrt{3}}{2}$, find the value of $cos\left( \frac{5\pi}{6}+\alpha\right) - sin^2\left(-\alpha+\frac{7\pi}{6}\right)$.
If $cos\alpha = \frac{2}{3}$ and $\alpha$ is an angle in the fourth quadrant, find the value of $\frac{sin(\alpha-2\pi)+sin(-\alpha-3\pi)cos(-\alpha-3\pi)}{cos(\pi -\alpha)-cos(-\pi-\alpha)cos(\alpha-4\pi)}$.

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