
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 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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