
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 $\overrightarrow{a} = \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right)$, $\overrightarrow{b} = (\sin x, \cos x)$, $f(x) = \overrightarrow{a} \cdot \overrightarrow{b} + 2$  
(1) Find the maximum and minimum values of $f(x)$ and the set of values of $x$ at which these extrema are achieved;  
(2) Determine the intervals of decrease for $f(x)$ on the interval $[0, 2\pi]$.

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