
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 the function $f(\alpha) = \frac {\sin(\alpha-\pi)\cos(2\pi-a)\sin(-\alpha+ \frac {3\pi}{2})\sin( \frac {5\pi}{2}+\alpha)}{\cos(-\pi -\alpha )\sin(-\pi -\alpha )}$,  
(1) Simplify $f(\alpha)$;  
(2) If $\cos\left(\frac {5\pi}{6}+2\alpha\right) = \frac {1}{3}$, find the value of $f\left(\frac {\pi}{12}-\alpha\right)$.

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