
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 $\overrightarrow {a}=(2\sin x, \cos x)$ and $\overrightarrow {b}=( \sqrt {3}\cos x, 2\cos x)$, define the function $f(x)= \overrightarrow {a}\cdot \overrightarrow {b}-1$, where $x\in\mathbb{R}$.
(I) Find the interval(s) where function $f(x)$ is monotonically increasing.
(II) In triangle $ABC$, let angles $A$, $B$, and $C$ correspond to sides $a$, $b$, and $c$, respectively. Given $f(B)=1$, $b= \sqrt {3}$, and $c=2$, find the area of triangle $ABC$.

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