
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 $$f(x)=4\sin x\cos\left(x+ \frac {\pi}{3}\right)+ \sqrt {3}$$, where $$x\in[0, \frac {\pi}{6}]$$.
(1) Find the range of the function $f(x)$;
(2) Given that the lengths of two sides, $a$ and $b$, of an acute triangle $\triangle ABC$ are the minimum and maximum values of the function $f(x)$ respectively, and the radius of the circumscribed circle of $\triangle ABC$ is $$\frac {3 \sqrt {2}}{4}$$, find the area of $\triangle ABC$.

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