
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 $0 < α < \dfrac {π}{2}$, $\sin α= \dfrac {4}{5}$, and $\tan (α-β)=- \dfrac {1}{3}$, find the value of $\tan β$ and compute the expression $\dfrac {\sin (2β- \dfrac {π}{2})\cdot \sin (β+π)}{ \sqrt {2}\cos (β+ \dfrac {π}{4})}$.

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