
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
(1) Given $\cos \left( \frac {\pi}{6}-\alpha \right)= \frac { \sqrt {3}}{2}$, find the value of $\cos \left( \frac {5}{6}\pi+\alpha \right)-\sin ^{2}\left(-\alpha+ \frac {7\pi}{6}\right)$.  
(2) 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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