
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 $f(\alpha)= \frac{\sin (\pi-\alpha)\cos (\alpha- \frac{\pi}{2})\cos (\pi+\alpha)}{\sin ( \frac{\pi}{2}+\alpha )\cos ( \frac{\pi}{2}+\alpha )\tan (3\pi +\alpha )}$,

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

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