
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 $\dfrac{\pi }{2} < \alpha < \pi$ and $\tan \alpha - \dfrac{1}{\tan \alpha} = -\dfrac{3}{2}$, find the value of $\tan \alpha$ and evaluate the expression $\dfrac{\cos (\dfrac{3\pi }{2}+\alpha )-\cos (\pi -\alpha )}{\sin (\dfrac{\pi }{2}-\alpha )}$.

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