
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 $f(\alpha)= \frac {\sin (\alpha-3\pi)\cos (2\pi-\alpha)\cdot \sin (-\alpha+ \frac {3}{2}\pi)}{\cos (-\pi -\alpha )\sin (-\pi -\alpha )}$.
(1) Simplify $f(\alpha)$;
(2) If $\alpha$ is an angle in the third quadrant, and $\cos (\alpha- \frac {3}{2}\pi)= \frac {1}{5}$, find the value of $f(\alpha)$;
(3) If $\alpha=-\frac {31\pi}{3}$, find the value of $f(\alpha)$.

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