
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: $f(\alpha)= \dfrac {\sin (4\pi-\alpha)\cos (\pi-\alpha)\cos ( \dfrac {3\pi}{2}+\alpha)\cos ( \dfrac {7\pi}{2}-\alpha)}{\cos (\pi +\alpha )\sin (2\pi -\alpha )\sin (\pi +\alpha )\sin ( \dfrac {9\pi}{2}-\alpha )}$  
$(1)$ Simplify $f(\alpha)$  
$(2)$ Find $f(- \dfrac {31}{6}\pi)$

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