
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
Evaluate the following:
1. Given $f(α)= \frac {2sin(π+α)cos(π-α)-cos(π+α)}{1+sin^{2}α+cos( \frac {3π}{2}+α)-sin^{2}( \frac {π}{2}+α)}(1+2sinα≠0)$, find the value of $f(- \frac {23}{6}π)$.
2. If $cos( \frac {π}{6}-α)= \frac { \sqrt {3}}{3}$, find the value of $cos( \frac {5π}{6}+α)-sin^{2}(α- \frac {π}{6})$.

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