
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 $f(\alpha)= \dfrac {\sin (7\pi-\alpha)\cdot \cos (\alpha+ \dfrac {3\pi}{2})\cdot \cos (3\pi+\alpha)}{\sin (\alpha - \dfrac {3\pi}{2})\cdot \cos (\alpha + \dfrac {5\pi}{2})\cdot \tan (\alpha -5\pi )}$.
$(1)$ Simplify $f(\alpha)$;
$(2)$ If $\alpha$ is in the second quadrant, and $\cos ( \dfrac {3\pi}{2}+\alpha)= \dfrac {1}{7}$, find the value of $f(\alpha)$.

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