
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 $\overrightarrow{a} = (\sin x, \sqrt{3})$ and $\overrightarrow{b} = (2\cos x, \sqrt{3})$. Let the function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$,

(1) Find the maximum value of $f(x)$.

(2) Find the interval of monotonic increase for $f(x)$.

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