
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 $y=4\cos^2x+4\sqrt{3}\sin x\cos x-2$, where $x\in \mathbb{R}$.

(1) Find the smallest positive period of the function;  
(2) Find the maximum value of the function and the corresponding value(s) of $x$;  
(3) Write down the interval(s) where the function is increasing.

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