
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 $\sin(α+ \frac {π}{2})=- \frac { \sqrt {5}}{5}, α∈(0,π)$, find:

1. The value of $\frac {cos^{2}( \frac {π}{4}+ \frac {α}{2})-cos^{2}( \frac {π}{4}- \frac {α}{2})}{sin(π-α)+cos(3π+α)}$
2. The value of $cos(2α- \frac {3π}{4})$

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