
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 $f(x)=4\sin x(\cos x-\sin x)+3$,
(I) Find the interval where $f(x)$ is monotonically decreasing when $x\in(0,\pi)$;
(II) If the range of $f(x)$ on $[0,\theta]$ is $[0,2\sqrt{2}+1]$, find the value of $\cos 2\theta$.

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