
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 $f(x)=\sqrt{3}\sin 2x - 2\sin^2 x + 2$, where $x\in R$.

(I) Find the interval where the function $f(x)$ is monotonically increasing, as well as the center of symmetry;

(II) If the graph of function $f(x)$ is shifted to the left by $m (m > 0)$ units to obtain function $g(x)$, and the graph of $g(x)$ is symmetric about the $y$-axis, find the minimum value of the real number $m$.

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