
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 $ \dfrac {3\pi}{4} < \alpha < \pi$, $\tan \alpha+ \dfrac {1}{\tan \alpha}=- \dfrac {10}{3}$.  
$(1)$ Find the value of $\tan \alpha$;  
$(2)$ Find the value of $ \dfrac {5\sin ^{2} \dfrac {\alpha}{2}+8\sin \dfrac {\alpha}{2}\cos \dfrac {\alpha}{2}+11\cos ^{2} \dfrac {\alpha}{2}-8}{ \sqrt {2}\sin (\alpha- \dfrac {\pi}{4})}$.

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