
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 $α$ is an angle in the third quadrant, find the value of the function 
$$f(α)= \frac {\sin(α- \frac {π}{2})\cos( \frac {3π}{2}+α)\tan(π-α)}{\tan(-α -π )\sin(-α -π )}.$$  
(1) Simplify $f(α)$;  
(2) If $f(α)= \frac {4}{5}$, find the value of $\tan α$.

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