
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]


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Suppose $\alpha$ is an angle in the third quadrant, the function $f(\alpha)$ is defined as $$f(\alpha)= \frac {\sin(\alpha - \frac {\pi}{2})\cos(\frac {3\pi}{2}+\alpha)\tan(\pi-\alpha)}{\tan(-\pi-\alpha)\sin(-\pi-\alpha)}.$$  
(1) Simplify $f(\alpha)$;  
(2) If $\cos(\alpha - \frac {3\pi}{2})= \frac {1}{5}$, find the value of $f(\alpha)$.

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