
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 $\overrightarrow{a}=(\sin x,\sin x), \overrightarrow{b}=( \sqrt {3}\cos x,\sin x)$,
(I) Define function $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}$, and find the interval where $f(x)$ is monotonically increasing;
(II) In $\triangle ABC$, acute angle $A$ satisfies $f(A)= \dfrac {3}{2}$, $b+c=4,a= \sqrt {7}$, find the area of $\triangle ABC$.

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