
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
(I) Given that $\cos (\pi+\alpha)=- \frac {1}{2}$, where $\alpha$ is an angle in the first quadrant, find the value of $\cos ( \frac {\pi}{2}+\alpha)$;
(II) Given that $\cos ( \frac {\pi}{6}-\beta)= \frac {1}{3}$, find the value of $\cos ( \frac {5\pi}{6}+\beta)\cdot \sin ( \frac {2\pi}{3}-\beta)$.

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