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

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