
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, $f(α)= \frac {\sin (π-α)\cdot \cos (2π-α)\cdot \tan (-α-π)}{\tan (-α )\cdot \sin (-π -α)}$.
(1) Simplify $f(α)$;
(2) If $\cos (α- \frac {3}{2}π)= \frac {1}{5}$, find the value of $f(α)$;
(3) If $α=-1860^{\circ}$, find the value of $f(α)$.

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