
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 that $\alpha$ is an angle in the third quadrant, $f(\alpha)= \dfrac {\sin (\alpha- \dfrac {\pi}{2})\cos ( \dfrac {3\pi}{2}+\alpha)\tan (\pi-\alpha)}{\tan (-\alpha -\pi )\sin (-\alpha -\pi )}$.
$(1)$ Simplify $f(\alpha)$;
$(2)$ If $f(\alpha)= \dfrac {4}{5}$, find $\tan \alpha$

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