
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]


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Given $$\text{f(x)} = 2 \sqrt {3}\cos^{2}{\text{x}} + 6\sin{\text{x}}\cos{\text{x}} - \sqrt {3}\ (\text{x} \in \mathbb{R})$$,
(1) Find the monotonically decreasing interval of function f(x) and describe how the graph of y=f(x) is obtained through a transformation of y=$$2 \sqrt {3}\sin{2\text{x}}$$;
(2) When $$\text{x} \in [0, \frac {\pi}{2}]$$, find the extreme values of function f(x) and the corresponding x values when the function takes the extreme values.

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