
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 the function $f(x)=\sin (2x-\frac{\pi }{4})$.

(Ⅰ) Find the intervals where $f(x)$ is decreasing;

(Ⅱ) If $\alpha \in (\frac{\pi}{2}, \pi)$, and $f(\frac{\alpha }{2}+\frac{\pi}{4})=\frac{2}{3}\cos (\alpha +\frac{\pi}{4})\cos 2\alpha$, find the value of $\sin \alpha -\cos \alpha$.

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