
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 $f(x) = 2\cos{x}\sin{x} + \sqrt{3}(2\cos^2{x} - 1)$.  
(1) Find the maximum value of $f(x)$.  
(2) Find the minimum positive period and the intervals of monotonic increase for $f(2x)$.

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