
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 $f(\alpha)= \frac{\sin (\frac{\pi}{2}-\alpha)\cos (10\pi-\alpha)\tan (- \alpha + 3\pi)}{\tan (\pi + \alpha)\sin (\frac{5\pi}{2} + \alpha)}$.
(1) Simplify $f(\alpha)$;
(2) If $\alpha \in (0, \frac{\pi}{2})$ and $\sin (\alpha - \frac{\pi}{6}) = \frac{1}{3}$, find the value of $f(\alpha)$.

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