
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 $f(x)=4\sin x\cos (x+\dfrac{\pi }{3})+\sqrt{3}$, where $x\in \left[ 0,\dfrac{\pi }{6} \right]$.

(I) Find the range of the function $f(x)$;

(II) The two sides of an acute triangle $\Delta ABC$, $a$ and $b$, are the minimum and maximum values of the function $f(x)$, respectively. The radius of the circumcircle of $\Delta ABC$ is $\dfrac{3\sqrt{2}}{4}$. Find the area of $\Delta ABC$.

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