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

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