
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]


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Given $f(α)= \frac {\sin ( \frac {π}{2}+α)\cdot \sin (2π-α)}{\cos (-π -α)\cdot \sin ( \frac {3}{2}π +α)}$,
$(1)$ If $α$ is an angle in the third quadrant, and $\cos (α- \frac {3}{2}π)= \frac {1}{5}$, find the value of $f(α)$;
$(2)$ If $f(α)=-2$, find the value of $2\sin α \cos α + \cos^2 α$.

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