
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 $y = 4\cos^2 x + 4\sqrt{3}\sin x \cos x - 2$, with $x \in \mathbb{R}$.
1. Find the smallest positive period of the function.
2. Find the maximum value of the function and the corresponding $x$ values.
3. Write the intervals on which the function is increasing.
4. Write the equations for the axes of symmetry of the function.

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