
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 vectors $\overrightarrow{a}=( \sqrt {3}\cos x,0)$, $\overrightarrow{b}=(0,\sin x)$, and the function $f(x)=( \overrightarrow{a}+ \overrightarrow{b})^{2} = \sqrt {3}\sin 2x$.

(I) Find the minimum value of the function $f(x)$ and the set of $x$ values when the minimum occurs.
(II) Find the interval where the function $f(x)$ is monotonically increasing.

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