
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 $f(\alpha)= \dfrac {\sin (\pi-\alpha)\cos (2\pi-\alpha)\cos (-\alpha+ \dfrac {3}{2}\pi)}{\cos ( \dfrac {\pi}{2}-\alpha)\sin (-\pi-\alpha)}$  
$(1)$ Simplify $f(\alpha)$;  
$(2)$ If $\alpha$ is an angle in the third quadrant, and $\cos (\alpha- \dfrac {3}{2}\pi)= \dfrac {1}{5}$, find the value of $f(\alpha)$;  
$(3)$ If $\alpha=- \dfrac {31}{3}\pi$, find the value of $f(\alpha)$.

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