
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 vectors $\overrightarrow{a}=( \frac {1}{2}, \frac { \sqrt {3}}{2})$ and $\overrightarrow{b}=(\sin x,\cos x)$, and the function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}+2$
(1) Find the maximum and minimum values of $f(x)$ and the set of $x$ values when these extreme values are obtained;
(2) Find the interval(s) where $f(x)$ is monotonically decreasing in the interval $[0,2π]$.

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