
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, and $f(α)= \frac{\sin (\frac{3π}{2}-α)\cos (\frac{π}{2}-α)\tan (-α+π)}{\sin (\frac{π}{2}+α)\tan (2π-α)}$.
(1) Simplify $f(α)$;
(2) If $α=- \frac{32}{3}π$, find the value of $f(α)$;
(3) If $f(α)= \frac{2\sqrt{6}}{5}$, find the value of $\cos (π+α)$.

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