
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 $f(x)=(a+2\cos ^{2} \frac {x}{2})\cos (x+ \frac {π}{2})$, and $f( \frac {π}{2})=0$.
(I) Find the value of the real number $a$;
(II) If $f( \frac {α}{2})=- \frac {2}{5}$, $α∈( \frac {π}{2},π)$, find the value of $\cos ( \frac {π}{6}-2α)$.

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