
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 $f(x) = 2\cos^2x + 2\sqrt{3}\sin x\cos x - 1$ ($x \in \mathbb{R}$).
1. Simplify $f(x)$ into the form $f(x) = A\sin(\omega x + \varphi)$ ($A > 0$, $\omega > 0$, $0 < \varphi < \frac{\pi}{2}$).
2. Find the intervals where the function $f(x)$ is increasing.

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