
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 $f(x)=2\cos^2x+ \sqrt{3}\sin 2x$, where $x\in\mathbb{R}$.
1. Find the maximum value of $f(x)$ and the corresponding set of values for $x$.
2. Determine the intervals on which $f(x)$ is increasing.

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