
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 $f(x)=\sin 2x-2\cos^2x,x\in R$.

(I) Find the interval where the function $f(x)$ is monotonically increasing.

(II) If $f(\frac{\alpha}{2})=\sqrt{2}-1$, find the value of $\frac{\sin 2\alpha}{\sin^4\alpha + \cos^4\alpha}$.

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